Conference Book(2nd Version)

CONTENT
1、Introduction ................................................................. 1
2、Outline of Program ..................................................... 4
3、Notations ...................................................................... 5
4、Chairs and Speakers ................................................... 6
5、Program ..................................................................... 7
6、Abstract of talks ........................................................ 13
7、List of the participants ............................................. 29
The 2014 International Conference on Tensors and Matrices and
their Applications (TMA2014)
Suzhou University of Science and Technology(USTS)
Suzhou, China, December 17-19,2014
 Invited Speakers(Alphabetically)
Z.-J. Bai (University of California at Davis, USA)
C.-J. Bu (Harbin Engineering University, Harbin, China)
A. Chang (Fuzhou University, Fuzhou, China)
Z.-W. Chen (Soochow University, Suzhou, China)
A. Cichocki (Riken Brain Science Institute, Japan)
J. Cooper (University of South Carolina, USA)
L. D. Lathauwer (University of Leuven, Belgium)
J. Ding (University of Souern Mississippi, USA)
L. Elden (Linkoping University, Sweden)
Y.-Z. Fan (Anhui University, Hefei, China)
Y.-B. Gao (North China University, Taiyuan, China)
E. K. Gnang (Princeton University, USA)
C.-Q. Gu (Shanghai University, Shanghai, China)
Z.-H. Huang (Tianjin University, Tianjin, China)
C-K Li (College of William and Mary, USA)
G. Li (University of New South Wales, Australia)
W. Li (South China Normal University, Guangzhou, China)
Y.-T. Li (Yunnan University, Kunming, China)
L.-H. Lim (Chicago University, USA)
M. Ng (HK Normal University, Hong Kong)
L.-Q. Qi (HK Polytechnic University, Hong Kong)
P. Semrl (University of Ljubljana, Slovenia)
N. Shaked-Monderer (The Max Stern Yezreel Valley College, Haifa, Israel)
J.-Y. Shao (Tongji University, Shanghai, China)
W.-Y. Sun (Nanjing Normal University, Nanjing, China)
E. Tyrtyshnikov (Russian Academy of Sciences, Russia)
Q.-W. Wang (Shanghai University,Shanghai, China)
Y.-M. Wei (Fudan University,Shanghai, China)
Q.-Z. Yang (Nankai University,Tianjin, China)
L.-P. Zhang (Tsinghua University,Beijing, China)
G.-L. Zhou (Curtin University, Australia)
1
 Organizing Committee
Honorary Chair Liqun Qi（The Hong Kong Polytechnic University）
Chairmen of Academic Committee
Richard A. Brauldi(Univ. of Wisconsin, Madison,USA）
Kung-ching Chang (Peking Univ.)
Chi-Kwong Li (College of William & Marry,USA)
Yong-Zhong Song (Nanjing Normal University)
Academic Committee

Zhaojun Bai, University of California at Davis, USA

A. Berman, Technion-Israel Institute of Technology, Israel

Zhongwen Chen, Soochow University, Suzhou, China

Lieven De Lathauwer, University of Leuven, Belgium

Lars Elden, Linkoping University, Sweden

M. Fiedler, Czek National Institue, Czek

Wen Li, South China Normal University, Guangzhou,China

Lek-Heng Lim, Chicago University, USA

Michael Ng, The Hong Kong Baptist University, Hong Kong

Peter Semrl, University of Ljubljana, Slovenia (President of ILAS),

Jiayu Shao, Tongji University, Shanghai,China

Qingwen Wang, Shanghai University, China

Guanglu Zhou, Curtin University, Australia
Chair of TMA2014 Jianrong Wu (Vice-president of USTS)
Local Chair

Zhengke Miao (Jiangsu Normal Univ., Xuzhou)

Yiming Wei (Fudan Univ., Shanghai)

Changqing Xu (USTS, Suzhou)

Endorsed by The International Linear Algebra Society (ILAS)
 Hosted by
 Sponsored by
 Supported by
 Registration/accommodation
Time：8:00am-22:00pm, Dec. 16, 2014
Location: Aster Trustel Hotel, Sanxiang Rd. 488, Suzhou.
2

Transportation
 From Suzhou Railway Station：Take Line 2 subway (MTR) from the station to
Sanxiang Rd. Exit 1.
 From Suzhou North Railway Station：Take Line 2 subway (MTR) from the station to
Sanxiang Rd.488, Exit 1.
 From Pudong/Hongqiao airport of Shanghai：Take the express train to Suzhou Railway
Station (30 min. or so), then take the subway Line 2 as mentioned above.
 From Sunan Shuofang airport (苏南硕放机场)：There are shuttles from the airport to
Sanxiang Plaza, Suzhou (about 40 min.).
CONTACT INFORMATION
Mr. Y. G. Gu (Tel: 13962185529) for accommodation/transportation/meeting venue etc.
Dr. C.Q. Xu (13812759081) for conference program
3
Outline of Program
 All the activities of TMA2014 except the banquet and city excursion will be done
within Aster Hotel, including breakfast, coffee break, lunch, dinner.
 The coffee/tea/cookie/fruit/ will be ready right outside each lecture hall.
 All the lunch/supper(except the banquet) are on the 1st floor and in buffet form.
 The banquet will be held in the 2nd flr of the Reception Center of USTS at 18:30pm,
Dec. 17, four shuttles are arranged at the gate of Aster at 17:40 Dec. 17
 The opening ceremony will be held from 8:00-8:30am of Dec. 17, in the
Multi-Functional Hall (MFH) located on the 3rd floor.
 All the Plenary talks (three mornings) are to be held in the Multi-Functional Hall
located on the 3rd floor.
 The three parallel sessions (including the invited session and contributed session) are
arranged respectively in VIP Hall (2nd floor), Rose Hall (2nd floor) and Conference
E-Room (4th floor). Please see the following table for more details.
4
Notations
Label
Meaning
Time
Room
Location
IPT1-1
1st
Invited Plenary Talk session on Dec.17
8:30--10:00
MFH
3rd flr
IPT1-2
1st Invited Plenary Talk session on Dec.17
10:15-12:15
MFH
3rd flr
IPT2-1
1st Invited Plenary Talk session on Dec.18
08:00-10:00
MFH
3rd flr
IPT2-2
2nd Invited Plenary Talk session on Dec.18
10:15-12:15
MFH
3rd flr
IPT3-1
1st Invited Plenary Talk session on Dec.19
08:00-10:00
MFH
3rd flr
IPT3-2
2nd Invited Plenary Talk session on Dec.19
10:15-12:15
MFH
3rd flr
IST1-1
1st Invited Session on Dec.17
14:00-16:05
VIP
2nd flr
IST1-2
2ndInvited Session on Dec.17
14:00-16:05
Rose
2nd flr
IST1-3
3rd Invited Session on Dec.17
14:00-16:05
E-Rm
4th flr
IST2-1
1st Invited Session on Dec.18
14:00-16:05
VIP
2nd flr
IST2-2
2nd Invited Session on Dec.18
14:00-16:05
Rose
2nd flr
IST2-3
3rd Invited Session on Dec.18
14:00-16:05
E-Rm
4th flr
CST1-1
1st Contributed Session on Dec.17
16:25-17:45
VIP
2nd flr
CST1-2
2ndContributed Session on Dec.17
16:25-17:45
Rose
2nd flr
CST1-3
3rd Contributed Session on Dec.17
16:25-17:45
E-Rm
4th flr
CST2-1
1st Contributed Session on Dec.18
16:25-17:45
VIP
2nd flr
CST2-2
2ndContributed Session on Dec.18
16:25-17:45
Rose
2nd flr
CST2-3
3rdContributed Session on Dec.18
16:25-17:45
E-Rm
4th flr
5
Chairs and Speakers
Program
IPT1-1
IPT1-2
IPT2-1
IPT2-2
IPT3-1
IPT3-2
IST1-1
IST1-2
IST1-3
IST2-1
IST2-2
IST2-3
CST1-1
CST1-2
CST1-3
CST2-1
CST2-2
CST2-3
Time
Chairs
Speakers
08:30-9:00
Jiayu Shao
Liqun Qi
09:00-9:30
Liqun Qi
Eugene Tyrtyshnikov
09:30-10:00
Yang Zhang
Peter Semrl
10:15--11:15
Michael Ng
Chi-Kwong Li,
11:15--12:15
Xiaodong Zhang
Zhaojun Bai,
Juan Manuel Pena
08:00-09:00
Peter Semrl
Yuhong Dai,
Naomi Shaked-Monderer
09:00-10:00
Zhengyue Zhang
Guoyin Li,
10:15--11:15
Liqun Qi
Jiu Ding, Wenyu Sun
11:15-12:15
Qin Ni
Sanzheng Qiao,
08:00-09:00
Musheng Wei
Yaotang Li, Chen Ling
09:00-10:00
Shangjun Yang
Changjiang Bu,
10:15--11:15
Yizheng Fan
Qingzhi Yang ,
11:15-12:15
Yubin Gao
An Chang,
14:00--15:15
Chen Ling
Qin Ni,
15:15-16:05
Yiju Wang
Yisheng Song,
14:00-15:15
Yu-Hong Dai
Minru Bai,
15:15-16:05
Minru Bai
Zhongming Chen,
14:00-15:15
Yimin Wei
Xiaodong Zhang, Chuanqing Gu, Yang Zhang
15:15-16:05
Yizheng Fan
Zhigang Jia, Junjie Yue
14:00--15:15
Nung-Sing Sze
Min Zhang, Zhen Chen, Qun Wang
15:15-16:05
Jianlong Chen
Maolin Che,
14:00--15:15
Zhenghai Huang
Pingzhi Yuan,
15:15-16:05
Zhongwen Chen
Lizhu Sun,
14:00--14:50
Wen Li
Changqing Xu,
14:50-16:05
Yaotang Li
Musheng Wei, Aijun Liu,
16:25-17:05
Guyan Ni
Bo Jiang,
17:05-17:45
Qin Ni
Tianwen Wei, Yiyong Li
16:25-17:05
Chunfeng Cui
Weiyang Ding,
17:05-17:45
An Chang
Shaohui Yu,
16:25-17:05
Shangjun Yang
Zhaolin Jiang,
17:05-17:45
Yisheng Song
Chengyi Zhang,
16:25-17:05
Chuanqing Gu
Volha Kushel，Sang-hyup
17:05-17:45
Yubin Gao
Jie Meng，Wei Chen
16:25-17:05
Zhaolin Jiang
Haibin Chen,
17:05-17:45
Jianli Zhao
Hongxia Xin，Tingting Xu
16:25-17:05
X. Liu, Y. Peng
17:05-17:20
C. Xu
6
Lieven De Lathauwer
Jiayu Shao
Yimin Wei
Wen Li
Qingwen Wang
Yizheng Fan
Yiju Wang,
Guoyin Li
Guyan Ni
Yannan Chen ,
Chunfeng Cui
Xiongjun Zhang
Chongguang Cao
Jiang Zhou, Lubing Cui
Jinjiang Yao
Jia Liu
Ziyan Luo
Zilong He
Jinshan Xie
Musheng Wei
Quanbin Zhang
Jianyong Wang
Program of TMA2014
Day 1, Dec 17 ,Wed.
8:00-8:30
IPT1-1
8:30-9:00
Opening Ceremony: Multi-Functional Hall（3rd flr）
Chair：Changqing Xu
Welcome Remarks by President of USTS, Yongzhong Song(Vice-President of China Computational
Mathematics Society), Liqun Qi (HK PolyU), Peter Semrl (President of ILAS)
Conference Photo
Chair: Jiayu Shao/Liqun Qi/Yang Zhang
Room：Multi-Functional Hall（3rd flr）
Liqun Qi, Hong Kong Polytechnic University
Chair: Jiayu Shao
Title: PSD Tensors, SOS Tensors and PNS Tensors ------ From Shallow Water to Deep Water
9:00-9:30
Eugene Tyrtyshnikov, Russian Academy of Sciences
Chair: Liqun Qi
Title: Low-rank matrices in the approximation of tensors and new optimization algorithms
9:30-10:00
Peter Semrl, Univ. of Ljubljana, Slovenia
Chair: Yang Zhang
Title: Adjacency preservers
Coffee break
Chair: Michael Ng/Xiaodong Zhang
Room：Multi-function Hall（3rd flr）
Chi-Kwong Li, College of William and Mary, USA
Chair: Michael Ng
Title: Tensor problems in quantum information science and projection methods
10:00-10:15
IPT1-2
10:15-10:45
10:45-11:15
Lieven De Lathauwer, Univ. of Leuven, Belgium
Chair: Michael Ng
Title: From tensor decomposition to coupled matrix/tensor decompositions
11:15-11:45
Zhaojun Bai, University of California at Davis, USA
Chair: Xiaodong Zhang
Title: Structured Computations of Block Matrices with Application in Quantum Monte Carlo Simulations
11:45-12:15
Juan Manuel Pena, University of Zaragoza, Spain
Chair: Xiaodong Zhang
Title: Subclasses of P-matrices, Kronecker product and tensors
12:15-14:00 Lunch
Afternoon Session
Topic
Location
Chair
IST1-1
Tensors and Optimizations
VIP Hall (2nd flr)
Chen Ling /Yiju Wang
14:00-14:25 Qin Ni, Nanjing University of Aeronautics and Astronautics,China
Chair: Chen Ling
Title: Quasi-Newton method for computing Z-eigenpairs of a real symmetric tensor
14:25-14:50
Yiju Wang, Qufu Normal University,China
Title: Nonsingular H-Tensors and Their Criteria
14:50-15:15
Guoyin Li, The University of New South Wales, Australia
Chair: Chen Ling
Title: Some Recent Advances of Polynomial Optimization: going back and forth between the ''polynomial world''
and the ''convexity world''
Yisheng Song, Henan Normal University,China
Chair: Yiju Wang
Title:Properties of Some Classes of Structured Tensors
15:15-15:40
15:40-16:05
16:05-16:25
CST1-1
16:25-16:45
Chair: Chen Ling
Guyan Ni, National University of Defense Technology
Chair: Yiju Wang
Title: Tensor representations of geometric measures of quantum entanglement
Coffee break
Topics
Location
Chair
nd
Nonnegative Tensors and related
VIP Hall (2 flr)
Guyan Ni/Qin Ni
Bo Jiang, Shanghai Univ. of Finance & Economics, China
Chair: Guyan Ni
7
Title: On the M-Rank of Even-Order Tensor and Its Applications in Low-Rank Tensor Optimization
16:45-17:05
Ziyan Luo, Beijing Jiaotong University, China
Chair: Guyan Ni
Title: Linear operators and positive semi-definiteness of symmetric tensor spaces
17:05-17:25
Tianwen Wei, Universite de Franche-Comte, France
Title：Von Neumann’s trace inequality for tensors
17:25-17:45
18:10-20:10
Chair: Qin Ni
Yiyong Li, Nankai University, China
Chair: Qin Ni
Title: A new definition of geometric multiplicity of tensor eigenvalues and some results based on it
Banquet
Topic
Location
Tensor Computations and Applications
Rose Hall (2nd flr)
Minru Bai, Hunan University, China
Title: A method of Computation of US-Eigenvalues of Complex Tensor
Chair
Yu-Hong Dai/Minru Bai
Chair: Yu-Hong Dai
14:25-14:50
Yannan Chen, Zhengzhou University, China
Title:Estimating Nonnegative Fiber Orientation Distribution Functions
Chair: Yu-Hong Dai
14:50-15:15
Chunfeng Cui, Chinese Academy of Sciences, China
Chair: Yu-Hong Dai
Title: A Feasible Trust-region Method for Calculating Extreme Z-eigenvalues of Symmetric Tensors
15:15-15:40
Zhongming Chen, Nankai University, China
Chair: Minru Bai
Title: Further results on B-tensors with application to the location of real eigenvalues
15:40-16:05
Xiongjun Zhang, Hunan University, China
Chair: Minru Bai
Title: A Corrected Procedure for Tensor Completion
Coffee break
Topic
Location
Chairs
Tensors and hypergraphs
Rose Hall (2nd flr)
Chunfeng Cui/J.M.Peña
Weiyang Ding, Fudan University, China
Chair: Chunfeng Cui
Title: Fast Hankel Tensor-Vector Product and Its Application to Exponential Data Fitting
IST1-2
14:00-14:25
16:05-16:25
CST1-2
16:25-16:45
16:45-17:05
Zilong He, South China Normal University, China
Title: A conjecture on the primitive degree of tensors
Chair: Chunfeng Cui
17:05-17:25
Shaohui Yu, Hefei Normal University, China
Title: Improved tensor decomposition for spectroscopy analysis
Chair: J.M.Peña
17:25-17:45
Jinshan Xie, Longyan University, China
Title: Spectral directed hypergraph theory via tensor
Chair: J.M.Peña
18:10-20:10
IST1-3
14:00-14:25
Banquet
Topic
Location
Matrices and Graphs
E-Room (4th flr)
Xiaodong Zhang, Shanghai Jiao Tong University, China
Title：The algebraic connectivity of graphs
Chairs
Yimin Wei / Yizheng Fan
Chair: Yimin Wei
14:25-14:50
Jiang Zhou, Harbin Engineering University, China
Title: Resistance distance and resistance matrix of a graph
Chair: Yimin Wei
14:50-15:15
Yang Zhang, University of Manitoba，Canada
Title: Computing MP pseudo inverses of polynomial matrices
Chair: Yimin Wei
8
15:15-15:40
Zhigang Jia, Jiangsu Normal University, China
Chair: Yizheng Fan
Title: Self-adjoint Matrix Polynomial Equation: Solvability Theory, Iteration Methods and Perturbation Analysis
15:40-16:05
Junjie Yue, Tsinghua University, China
Chair: Yizheng Fan
Title: The largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths
16:05-16:25
CST1-3
Coffee break
Topic
Location
Chair
th
Hypergraphs, matrices and Patterns
E-Room (4 flr)
Shangjun Yang / Yisheng Song
Zhaolin Jiang, Linyi University, China
Chair: Shangjun Yang
Title: Norm estimates of ω-circulant operator matrices and isomorphic operators for ω-circulant algebra
16:25-16:45
16:45-17:05
Musheng Wei, Liaocheng University, China
Title:
Chair: Shangjun Yang
17:05-17:25
Chengyi Zhang, Xi'an Polytechnic University, China
Title: On equally absolute sum matrices/tensors
Chair: Yisheng Song
17:25-17:45
Quanbin Zhang, Anhui University, China
Chair: Yisheng Song
Title: Counting extreme U1 matrices and characterizing the quadratic doubly stochastic matrices
18:10-20:10
Banquet
Day 2, Dec 18 (Thursday)
Invited Plenary Talks (PTs)
IPT2-1
Room：Multi-function Hall（3rd flr）
8:00-8:30
Yuhong Dai, Chinese Academy of Sciences, China
Title: All Real Eigenvalues of Symmetric Tensors
Chairs: Peter Semrl / Zhengyue Zhang
Chair: Peter Semrl
8:30-9:00
Naomi Shaked-Monderer, The Max Stern Yezreel Valley College, Israel
Title: Nearly Positive Matrices
9:00-9:30
Guoyin Li, Univ. of New South Wales, Australia
Chair: Zhengyue Zhang
Title: The Maximum Eigenvalue of a Symmetric Tensor: a Polynomial Optimization Approach
9:30-10:00
Jiayu Shao, Tongji University, China
Title: Some results in extremal spectral hypergraph theory
Coffee break
Room：Multi-function Hall（3rd flr）
Jiu Ding, University of Southern Mississippi, USA
Title: Solving the Yang-Baxter-type Matrix Equation
10:00-10:15
IPT2-2
10:15-10:45
Chair:
Chair:
Peter Semrl
Zhengyue Zhang
Chairs: Liqun Qi /Qin Ni
Chair: Liqun Qi
10:45-11:15
Wenyu Sun, Nanjing Normal University, Nanjing, China
Chair: Liqun Qi
Title：A Novel Regularized Alternating Least Squares Algorithm with Global Convergence for Canonical
Tensor Decomposition
11:15-11:45
Sanzheng Qiao, University of Mcmaster, Canada
Chair:
Title: Structured condition numbers for symmetric algebraic Riccati equations
Qin Ni
11:45-12:15
Yimin Wei, Fudan University, China
Title: Generalized Tensor Eigenvalue Problems
Lunch break
Qin Ni
12:15-14:00
9
Chair:
Afternoon Session
Topic
Location
IST2-1
Tensors and Optimizations
VIP Hall (2nd flr)
14:00-14:25 Min Zhang, Tianjin University, China
Title:Tensor Completion via Iterative Hard Thresholding
Chairs
Nung-Sing Sze / Jianlong Chen
Chair: Nung-Sing Sze
14:25-14:50
Zhen Chen, Guizhou Normal University, China
Title: Implicit Conjugate Gradient Method for Sylvester Tensor Equation
Chair: Nung-Sing Sze
14:50-15:15
Qun Wang, The Hong Kong Polytechnic University, China
Title: Are There Sixth Order Three Dimensional PNS Hankel Tensors?
Chair: Nung-Sing Sze
15:15-15:40
Maolin Che, Fudan University, China
Title:Positive Definite Tensors to Nonlinear Complementarity Problems
Chair: Jianlong Chen
15:40-16:05
Chongguang Cao, Heilongjiang University ,China
Title: Induced Maps Preserving Involutory Matrices Over Fields
Coffee break
Topic
Location
Matrix equation and matrix function
VIP Hall (2nd flr)
16:05-16:25
CST2-1
Chair: Jianlong Chen
Chairs
Chuanqing Gu/Yubin Gao
16:25-16:45
Volha Kushel, Shanghai Jiao Tong University, China
Title: On some new stable classes of P-matrices
16:45-17:05
Sang-hyup, Pusan National University, Korea
Chair: Chuanqing Gu
Title: The existence and convergence of two iterations for differentiable order-convex matrix functions
17:05-17:25
Jie Meng, Pusan National University, Korea
Title: The positive definite solution to a nonlinear matrix equation
17:25-17:45
Wei Chen, HK University of Science and Technology, China
Chair: Yubin Gao
Title: Existence Condition for (0,1)-Matrices with Given Row Sums and Certain Fixed Zeros
18:00-20:00
IST2-2
Dinner
Topic
Location
Chairs
Problems on various tensors
Rose Hall (2nd flr)
Zhenghai Huang/Zhongwen Chen
Pingzhi Yuan, South China Normal University, China
Chair: Zhenghai Huang
Title: Some results and open problems on the primitive degree of nonnegative tensors
14:00-14:25
Chair: Chuanqing Gu
Chair: Yubin Gao
14:25-14:50
Lubing Cui,Henan Normal University, China
Title: An Eigenvalue Problem for Even Order Tensors
14:50-15:15
Lizhu Sun, Harbin Institute of Technology , China
Chair: Zhongwen Chen
Title: Some results on the generalized inverse of tensors and idempotent tensors
15:15-15:40
Jinjiang Yao, Linyi University,China
Chair: Zhongwen Chen
Title: On Skew Circulant Type Matrices Involving any Continuous Pell Numbers
16:05-16:25
CST2-2
Coffee break
Topic
Structure matrices and cyclic matrices
Location
Rose Hall (2nd flr)
10
Chair: Zhenghai Huang
Chair
Zhaolin Jiang/Jianli Zhao
16:25-16:45
Haibin Chen, The Hong Kong Polytechnic University, China
Chair: Zhaolin Jiang
Title: Positive Definiteness and Semi-Definiteness of Even Order Symmetric Cauchy Tensors
16:45-17:05
Jianyong Wang, Linyi University, China
Title: The Chebyshev Skew Circulant Type Matrices With Polynomials
17:05-17:25
Hongxia Xin, Linyi University, China
Chair: Jianli Zhao
Title: The Determinants, Inverses of Gaussian Fibonacci ω-Circulant and Left ω-Circulant Matrices
17:25-17:45
Tingting Xu , Linyi University, China
Title: TBD
18:10-20:10
IST2-3
14:00-14:25
Chair: Zhaolin Jiang
Chair: Jianli Zhao
Dinner
Topic
Location
Mischievous
E-Room (4th flr)
Changqing Xu, The Suzhou University of Science and Technology, China
Title: Vandermonde Tensors and their applications
Chairs
Wen Li/Yaotang Li
Chair: Wen Li
14:25-14:50
Jia Liu, Univeristy of West Florida, Florida, USA
Title: An effective preconditioner for the incompressible fluid problems
Chair: Wen Li
14:50-15:15
Yonghui Ling, Zhejiang University, China
Title: TBD
Chair: Yaotang Li
15:15-15:40
Aijun Liu, Qufu Normal University, China
Title: TBD
15:40-16:05
Qi Zhao, Soochow University, China
Title: TBD
16:05-16:25
CST2-3
Coffee break
Topic
Free discussion
Anyone is welcome.
Blanked specifically for open discussion
16:25-17:05
Chair: Yaotang Li
Chair: Yaotang Li
Location
E-Room (4th flr)
Chair
Xiaoji Liu/Yanling Peng/C. Xu
Chair: Xiaoji Liu/ Yanling Peng
17:05-17:20
18:10-20:10
Dinner
Day 3, Dec 19 (Friday), 2014
IPT3-1
8:00-8:30
Rm：Multi-function Hall
Yaotang Li, Yunan University, China
Title： Double B-tensors and quasi-double B-tensors
8:30-9:00
Chen Ling, Hangzhou Dianzi University, China
Chair: Musheng Wei
Title: Standard bi-quadratic optimization problem and its approximation analysis
9:00-9:30
Changjiang Bu, Harbin Engineering University, China
Title: Some spectral properties of uniform hypergraphs
11
Chairs: Musheng Wei / Shangjun Yang
Chair: Musheng Wei
Chair: Shangjun Yang
9:30-10:00
Wen Li, South China Normal University, China
Title: Z-eigenpair bounds for an irreducible nonnegative tensor
10:00-10:15
IPT3-2
10:15-10:45
Coffee/Tea Break
Chairs: Yizheng Fan / Yubin Gao
Rm：Multi-function Hall
Qingzhi Yang, Nankai University, China
Chair: Yizheng Fan
Title: Some properties of nonnegative tensor eigenvalues and an algorithm solving the spectral radius
10:45-11:15
Qingwen Wang, Shanghai University, China
Chair: Yizheng Fan
Title: A simultaneous decomposition of seven matrices over the real quaternion algebra
11:15-11:45
Chuanqing Gu,Shanghai University, China
Chair: Yubin Gao
Title: Flexible global generalized Hessenberg methods for linear systems with multiple right-hand sides
11:45-12:15
Yizheng Fan, Anhui University, China
Chair: Yubin Gao
Title：On the Spectral Radius of a Class of Non-Odd-Bipartite Even Uniform Hypergraphs
12:15-13:30 Lunch
Afternoon
City Excursion: Suzhou Museum
Note:
1) You can sign up at the registration desk for the tour of Dec. 20-21.
2) If you need invoice, please tell us at the registration desk on Dec 16.
12
Chair: Shangjun Yang
The 2014 International Conference on Tensors, Matrices and their
Applications: Abstracts
1.Plenary Talks
Title Structured Computations of Block Matrices with Application in Quantum Monte Carlo Simulations
Speaker Zhaojun Bai, University of California, Davis
Abstract A block matrix can be regarded as a reshaped fourth-order tenor. A properly structured computation of the block matrix provides insight into the tensor and vice versa. In this talk, we focus on structured
computations of block p-cyclic matrices. We present our recent synergistic effort in developing numerical
stable and high-performance structured computations of block p-cyclic matrices and their applications in
the fourth-order tensor computations arising from quantum Monte Carlo simulations of the Hubbard model
in computational solid state physics.
Title Some Spectral Properties of Uniform Hypergraphs
Speaker Changjiang Bu, Harbin Engeneerine University, China
Abstract For a k-uniform hypergraph H, we obtain some trace formulas for the Laplacian tensor of H,
Pn
which imply that i=1 dsi (s = 1, . . . , k) is determined by the Laplacian spectrum of H, where d1 , . . . , dn
is the degree sequence of H. Using trace formulas for the Laplacian tensor, we obtain expressions for some
coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations
of odd-bipartite hypergraphs, and give some spectral properties of power hypergraphs. This is a joint work
with Zhou, Sun and Wang.
Title Tensor Spectra of Uniform Hypergraphs
Speaker An Chang, Fuzhou University, China
Abstract In the recent years, the tensor spectra theory of hypergraphs has been well developed due to its
theoretical significance and applications in many disciplines. In this talk, we present some spectral properties
on the Z-eigenvalues and H- eigenvalues of the adjacency tensor of a uniform hypergraph.
Title All Real Eigenvalues of Symmetric Tensors
Speaker Yuhong Dai, Chinese Academy Science, China
Abstract This paper studies how to compute all real eigenvalues, associated to real eigenvectors, of a
symmetric tensor. As is well known, the largest or smallest eigenvalue can be found by solving a polynomial
optimization problem, while the other middle ones cannot. We propose a new approach for computing all
real eigenvalues sequentially, from the largest to the smallest. It uses Jacobian semidefinite relaxations in
polynomial optimization. We show that each eigenvalue can be computed by solving a finite hierarchy of
semi definite relaxations. Numerical experiments are presented to show how to do this. This is a joint work
with Chun-Feng Cui and Jiawang Nie.
Title From Tensor Decomposition to Coupled Matrix/Tensor Decompositions
Speaker Lieven De Lathauwer, University of Leuven, Belgium
Abstract Decompositions of higher-order tensors are becoming more and more important in signal processing, data analysis, machine learning, scientific computing, optimization and many other fields. As a current
trend, coupled matrix/tensor decompositions (i.e., decompositions of multiple matrices and/or tensors with
one or more factors in common) are now emerging. Applications can be found in various fields and include
recommender systems, advanced array processing systems, multimodal biomedical data analysis and data
completion. We give a short overview and discuss the state-of-the-art in the generalization of results for
13
tensor decompositions to coupled matrix/tensor decompositions. We briefly discuss the remarkable uniqueness properties, which make these decompositions important tools for signal separation. Factor properties
(such as orthogonality, but also nonnegativity, exponential structure, etc.) may be imposed when useful but
are not required for uniqueness per se. Also remarkable, in the exact case the decompositions may under
mild conditions be computed using only tools from standard linear algebra. We touch upon the computation
of inexact decompositions via numerical optimization. We illustrate some of the ideas using Tensorlab, a
Matlab toolbox for tensors and tensor computations that we have recently released, and of which version 2
provides a comprehensive framework for the computation of (possibly constrained) coupled matrix/tensor
decompositions.
Title Solving the Yang-Baxter-type Matrix Equation
Speaker Jiu Ding, University of Southern Mississippi, USA
Abstract Finding nontrivial solutions of nonlinear matrix equations is often difficult in linear algebra. We
use the homogeneous quadratic matrix equation
AXA = XAX
as the topic of this talk to see how we deal with this particular nonlinear matrix equation. Here A is a known
square matrix and X is the unknown one. Because of its similarity to the classic Yang-Baxter equation in
format, the equation may be called the Yang-Baxter-type matrix equation. We shall give an overview of
our research on solving the Yang-Baxter-type matrix equation in the past couple of years, mostly about
commuting solutions in various cases, and our hope is to attract linear algebraists’ attention for finding all
solutions of this challenging matrix equation.
Title Tensor problems in quantum information science and projection methods
Speaker Chi-Kwong Li, College of William and Mary, USA
Abstract We consider problems in quantum information science involving tensors, and discuss how to use
projection methods in the study. Recent results and open problems will be mentioned. Extension of the
techniques to other problems involving tensors will be considered.
Title The Maximum Eigenvalue of a Symmetric Tensor: a Polynomial Optimization Approach
Speaker Guoyin Li, University of New South Wales, Australia
Abstract Determining the maximum eigenvalue of a symmetric tensor is of great importance in applied
mathematics and engineering, and is an intrinsically hard problem. This problem arises in various important
engineering applications and provides a rich and fruitful interaction between multilinear algebra and global
optimization. We establish some new theoretical results on the maximum eigenvalue function of an even order
symmetric tensor via a polynomial optimization approach. In particular, for an mth-order n-dimensional
symmetric tensor A, we establish that the maximum eigenvalue function are ρth-order semismooth at A
and provide explicit estimates (in terms of the order m and dimension n) of the exponent ρ. Moreover,
we provide a tractable extension of Yuan’s alternative theorem from matrix to the tensor setting. As a
consequence, we show that the maximum eigenvalue of a symmetric tensor with suitable sign structure (or
more explicitly, with essentially non-negative coefficients) can be found by solving a single semi-definite
programming problem. If time allows, we will also discuss some of our recent progress in understanding
positive semi-definite Hankel tensors. This talk is based on joint works with S. Hu, B.S. Mordukhovich, L.Q.
Qi, Y. Song, Q. Wang, Y. Xu, and G. Yu.
Title Z-eigenpair bounds for an irreducible nonnegative tensor*
Speaker Wen Li, South China Normal University, China
Abstract In this talk, we discuss the Z-eigenpair of a tensor, in particular, an irreducible nonnegative
tensor. We present some bounds for the eigenvector and Z-spectral radius. The proposed bounds improve
some existing ones. *joint work with DD Liu and SW Vong
14
Title Double B-tensors and Quasi-double B-tensors
Speaker Yaotang Li, Yunan University,China
Abstract In this talk, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors,
give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with Btensors and positive definite tensors and proved that even order symmetric double B-tensors and even order
symmetric quasi-double B-tensors are positive definite. These give some checkable sufficient conditions for
the positive definiteness of tensors.
Title Standard Bi-quadratic Optimization Problem and Its Approximation Analysis
Speaker Chen Ling, Hangzhou Dianzi University, China
Abstract We consider the problem of solving a standard bi-quadratic programming (StBQP), which is NPhard. We first present some lower bounds for the optimal value of the considered problem, each of which has
a simple closed-form representation and can be computed efficiently. Secondly, we study the approximation
solution and relative approximation ratio of the considered problem. Finally, after reformulating the original
problem as an equivalent co-positive tensor programming, we show how to approximate the optimal solution
by approximating the cone of co-positive tensors via a serial polyhedral cones. The established quality of
approximation shows that, a polynomial time approximation scheme (PTAS) for solving StBQP exists. Some
numerical examples are provided to illustrate our approach.
Title Subclasses of P-Matrices, Kronecker Product and Tensors
Speaker Juan Manuel Pena, University of Zaragoza, Spain
Abstract A P-matrix is a matrix with all its principal minors positive. Several subclasses of P-matrices
are considered in this talk. Some properties concerning with the Kronecker product of matrices in these
subclasses and with their extension to tensors are analyzed.
Title PSD Tensors, SOS Tensors and PNS Tensors —— From Shallow Water to Deep Water
Speaker Liqun Qi, Hong Kong Polytechnical University
Abstract The problem for determining a given even order symmetric tensor is positive semi-definite (PSD)
or not has important applications in engineering and science. In general, this problem is NP-hard. However,
for special tensor classes, such as even order symmetric Z tensors, this problem is polynomial time solvable.
In 2014, more classes of structured tensors have been identified, either such tensors are easily to be identified,
and they are PSD or positive definite in the even order symmetric case, or there are easily checkable conditions
to identify such tensors are PSD or not. The former includes Hilbert tensors, diagonally dominated tensors,
B tensors, double B tensors, quasi-double B tensors and H + tensors. The latter includes Cauchy tensors.
On the other hand, a new class of PSD tensors, called SOS (sum-of-squares) tensors, was introduced. SOS
tensors are PSD tensors, but not vice versa. SOS tensors are connected with SOS polynomials, which
are significant in polynomial theory and polynomial optimization. In particular, the problem to identify a
given general even order symmetric tensor is PSD or not is NP-hard, while the problem to identify a given
general even order symmetric tensor is SOS or not is equivalent to solving a semi-definite linear programming
problem, thus not NP-hard, but polynomial time solvable. Very recently, two important structured tensors strong Hankel tensors and positive Cauchy tensors, are shown to be SOS. However, not all the PSD tensors
are SOS tensors. This was first shown by Hilbert. PSD non-SOS (PNS) tensors do exist. The most famous
one is the Motzkin tensor. Now, a great interest is to identify structured tensors which are PNS-free. If
a class of structured tensors are PNS-free, then the problem for determining a given even order symmetric
tensor in that class is PSD or not is polynomial-time solvable. An interesting problem is: are Hankel tensors
PNS-free? Hankel tensors arise from signal processing and other applications. Until now, we do not know
whether Hankel tensors are PNS-free or not. A serious investigation on this problem is going on.
15
Title Structured Condition Numbers for Symmetric Algebraic Riccati Equations
Speaker Sanzheng Qiao, University of Mcmaster, Canada
Abstract Algebraic Riccati equations arise in optimal control problems in continuous and discrete time.
With multiple state variables and multiple control variables, the Riccati equations are matrix equations.
Perturbation analysis reveals the sensitivity of the solution to the input data. Assuming the structure of the
perturbation is the same as that of the data, we present a structured perturbation analysis of the continuous
and discrete symmetric algebraic Riccati equations. We define and derive structured normwise, mixed, and
componentwise condition numbers for symmetric algebraic Riccati matrix equations using the Kronecker
product.
Title Adjacency Preservers
Speaker Peter Semrl, University of Ljubljana, President of ILAS, Slovenia
Abstract Two matrices are said to be adjacent if their difference is of rank one. The famous Chinese mathematician Luogeng Hua provedseveral theorems nowadays known as the fundamental theorems of geometry of
matrices describing the general form of adjacency preservers on various matrix spaces. I will discuss several
improvements of his results and applications in mathematical physics and geometry.
Title Nearly Positive Matrices
Speaker Naomi Shaked-Monder, Israel Institute of Technology, Israel
Abstract A matrix is nearly positive if it can be made positive by pre-multiplying it by orthogonal matrices
as close to the identity as one wishes. That is, if there exists a sequence of orthogonal matrices converging
to the identity matrix, each mapping all the columns of the matrix simultaneously into the interior of the
nonnegative cone.
Title Some Results in Extremal Spectral Hypergraph Theory.
Speaker Jiayu Shao, Tongji University, Shanghai,China
Abstract The extremal spectral graph theory is one of the most popular research area in spectral graph
theory. But for spectral hypergraph theory, up to now we have not yet seen much research work in the
area of extremal spectral hypergraph theory. Also, most of the useful methods used in extremal spectral
graph theory (eg. edge-moving operation, edge-grafting operation and so on) have not been generalized
to extremal spectral hypergraph theory. In this paper, we generalize some useful methods (operations) in
extremal spectral graph theory from graphs to hypergraphs, and solve some extremal spectral problems for
some special classes of hypergraphs (such as supertrees and hypertrees) and some special types of spectrum
(such as the adjacency spectral radius, signless Laplacian spectral radius and incidence Q∗ -spectral radius),
by using these generalized operations on hypergraphs. We also mention some unsolved problems.
Title A Novel Regularized Alternating Least Squares Algorithm with Global Convergence for Canonical
Tensor Decomposition
Speaker Wenyu Sun, Nanjing Normal University, China
Abstract The regularization method could deal with the swamp effect of alternating least squares (ALS)
algorithms for tensor decomposition. The regularization term is a norm of the difference between the solution
and the current iterate. In this paper, we show that the norm could be weakened to a seminorm so the
selection of the regularization term could be more flexible. To overcome the swamp effect and avoid the
drawback that the Hessian of the subproblem may get close to singular in the iterative procedure, we propose
a seminorm regularized ALS algorithm for solving the canonical tensor decomposition. Moreover, in new
algorithm, we introduce a novel extrapolation in the update of each mode factor which makes an immediate
impression on the update of subsequent ones. Under some mild assumptions, the global convergence of new
algorithm with a seminorm regularization and the novel extrapolation is established. Numerical experiments
on synthetic and real-world problems show that the new method is efficient and promising.
16
Title Low-rank Matrices in the Approximation of Tensors and New Optimization Algorithms
Speaker Eugene Tyrtyshnikov, Russian Academy of Sciences
Abstract The construction of most successful numerical algorithms for multi-dimensional problems usually
involves multi-index arrays, also called tensors, and capitalizes on those tensor decompositions that reduce,
one way or another, to low-rank matrices associated with the given tensors. It can be argued that the most
of recent progress is due to the TT and HT decompostions. The differences between the two decompositions
may look as rather subtle, because the both are based on the same dimensionality reduction tree and exploit
seemingly the same idea. In this talk, we analyze the differences between the two decompositions and present
them in a clear and simple way. Besides that, we demostrate some new applciations of tensor approximations
in numerical analysis, in particular the docking drug-design problem, parameter identification in biological
models, Smoluchowski equations etc.
Title A Simultaneous Decomposition of Seven Matrices over the Real Quaternion Algebra
Speaker Qingwen Wang, Shanghai University, China
Abstract Let H be the real quaternion algebra and Hn×m denote the set of all n × m matrices over H.
In this paper, we construct a simultaneous decomposition of seven general real quaternion matrices with
compatible sizes: A ∈ Hm×n , B ∈ Hm×p1 , C ∈ Hm×p2 , D ∈ Hm×p3 , E ∈ Hq1 ×n , F ∈ Hq2 ×n , G ∈ Hq3 ×n . As
applications of the simultaneous matrix decomposition, we give solvability conditions, general solutions, as
well as the range of ranks of the general solutions to the following two real quaternion matrix equations
BXE + CY F + DZG = A and BX + W E + CY F + DZG = A, where A, B, C, D, E, F, and G are given
real quaternion matrices.
Title Generalized Tensor Eigenvalue Problems
Speaker Yimin Wei, Fudan University, China
Abstract This talk is devoted to the generalized tensor eigenvalue problems. We focus on the properties
and perturbations of the spectra of regular tensor pairs. Employing different techniques, we extend several
classical results from matrices or matrix pairs to tensor pairs, such as the Gershgorin circle theorem, the
Perron-Frobenius theorem, the Bauer-Fike theorem, the Rayleigh-Ritz theorem, the backward error analysis,
the componentwise distance of a nonsingular tensor to singularity, etc. Some of these results preserve their
original forms, whereas the others change when being extended.
Title Some Properties of Nonnegative Tensor Eigenvalues and an Algorithm Solving the Spectral Radius
Speaker Qingzhi Yang, Nankai University, China
Abstract In this talk I will introduce some properties of nonnegative tensor eigenvalues, including the check
of nonnegative irreducible tensor, monotonicity of spectral radius of nonnegative tensor and the distribution
of eigenvalues over spectral circle and geometric simplicity of spectral radius. Ill also introduce a method for
finding the spectral radius of nonnegative tensor and related properties.
Title On the Spectral Radius of a Class of Non-Odd-Bipartite Even Uniform Hypergraphs
Speaker Yizheng Fan, Anhui University, China
Abstract In order to investigate the non-odd-bipartiteness of even uniform hypergraphs, we introduce a
class of k-uniform hypergraphs G, called (k, k2 )-hypergraphs, which satisfy the property: k is even, every edge
e of G can be divided into two disjoint k2 -vertex sets say e1 and e2 and for any edge e0 incident to e, e∩e0 = e1
or e2 . Such graph G can be constructed from a simple graph, which is called the underlying graph of G.
We show that G is non-odd-bipartite if and only if the underlying graph of G is non-bipartite. We obtain
some results for the spectral radius of weakly irreducible nonnegative tensors, and use them to discuss the
perturbation of the spectral radius of the adjacency tensor or signless Laplacian tensor of a (k, k2 )-hypergraph
after an edge is subdivided. Finally we show that among all non-odd-bipartite (k, k2 )-hypergraphs with n
17
half edges, the minimum spectral radius of the adjacency tensor (respectively, signless Laplacian tensor) is
achieved uniquely for Cn when n is odd and for Cn−1 + e when n is even.
Title Computing MP Pseudo Inverses of Polynomial Matrices
Speaker Yang Zhang, University of Manitoba, Canada
Matrices with non commutative entries has a long research history, at least dated back to Jacobson’s seminal
work in 1940s. In past ten years, these matrices have attracted more and more people in computer algebra area, and many important properties have been discussed by using symbolic computation methods, for
example, various fast algorithms for computing Hermite forms and Smith forms for Ore matrices. In this
paper, we consider Moore-Penrose pseudo inverse of Ore matrices and quaternion polynomial matrices. It
is well-known that every matrix over a field has a MP pseudo inverse. But it is not true for Ore matrices
in general. At first, we use blocked matrices and GCD computations to give some sufficient and necessary
conditions for Ore matrices to have MP pseudo inverses. Then when MP pseudo inverses exist, we develop
algorithms to compute them. All algorithms are implemented in the symbolic programming language Maple,
and tested on examples.
2. Session Talks
Title A method of Computation of US-Eigenvalues of Complex Tensor
Speaker Minru Bai, Hunan University, China
Abstract US-eigenvalues of complex tensor are related to the geometric measures of entanglement problems,
which plays an important role in the quantum information theory. In this paper, we propose an algorithm
to compute the US-eigenvalues of complex tensor and prove the convergence of the algorithm. Numerical
results demonstrate the effectiveness of the proposed algorithm.
Title Induced Maps Preserving Involutory Matrices Over Fields
Speaker Chongguang Cao, Heilongjiang University
Abstract Let Mn (F) be a set of all n × n matrices over a field F, where the integer n ≥ 2. We say that
a map f : Mn (F) → Mn (F) is induced by functions {fij |i, j ∈ [1, n] = {1, 2 · · · n}} on F, if f is defined by
f : A = [aij ] 7→ f (A) = [fij (aij )], ∀A ∈ Mn (F). An induced map f : Mn (F) → Mn (F) is called an involution
preserver if A2 = In implies (f (A))2 = In . In this paper, we give the forms of induced maps preserving
involutory matrices over F , which generalize the results of the induced maps preserving inverse matrices.
Title Positive Definite Tensors to Nonlinear Complementarity Problems
Speaker Maolin Che, Fudan University,China
Abstract The main purpose of this note is to investigate some kinds of nonlinear complementarity problems
(NCP). For the structured tensors, such as, symmetric positive definite tensors and copositive tensors, we
derive the existence theorems on a solution of these kinds of nonlinear complementarity problems. We prove
that a unique solution of the NCP exists under the condition of diagonalizable tensors.
Title Further results on B-tensors with application to the location of real eigenvalues
Speaker Zhongming Chen, Nankai University, China
Abstract In this paper, we give a further study on B-tensors. And doubly B-tensors are introduced, which
contain B-tensors. We show that they have similar properties, including their decompositions and strong
relationship with strictly (doubly) dominated tensors. As an application, the properties of B-tensors are used
to localize real eigenvalues of some tensors, which can be very useful in verifying the positive semi-definiteness
of a tensor.
18
Title Positive Deniteness and Semi-Deniteness of Even Order Symmetric Cauchy Tensors
Speaker Haibin Chen, The Hong Kong Polytechnic University
Abstract Motivated by symmetric Cauchy matrices, we dene symmetric Cauchy tensors and their generating
vectors in this paper. Hilbert tensors are symmetric Cauchy tensors. An even order symmetric Cauchy tensor
is positive semi-denite if and only if its generating vector is positive. An even order symmetric Cauchy tensor
is positive denite if and only if its generating vector has positive and mutually distinct entries. This extends
Fiedler’s result for symmetric Cauchy matrices to symmetric Cauchy tensors. Then, it is proven that the
positive semi-deniteness character of an even order symmetric Cauchy tensor can be equivalently checked
by the monotone increasing property of a homogeneous polynomial related to the Cauchy tensor. The
homogeneous polynomial is strictly monotone increasing in the nonnegative orthant of the Euclidean space
when the even order symmetric Cauchy tensor is positive denite. At last, bounds of the largest H-eigenvalue
of a positive semi-denite symmetric Cauchy tensor are given and several spectral properties on Z-eigenvalues
of odd order symmetric Cauchy tensors are shown. Further questions on Cauchy tensors are raised.
Title Some inequalities for the principal submatrices of invertible Hermitian matrices with the applications
to the Hadamard products
Speaker Meixiang Chen, Putian University, China
Abstract Firstly, the inequalities for the principal submatrices of invertible Hermitian matrices are obtained.
Then without positive definiteness demanded in the present papers, some inequalities for the Hadamard
products of invertible Hermitian matrices are shown. As positive matrices naturally satisfy the added
constraints, these results generalize and improve the corresponding results in the present papers. Beyond
that, as the all discussions are started from original inequalities, then the sufficient and necessary conditions
for the equations in these inequalities held are given. The results indicate that, with no demand positive
definiteness, these forward and backward inequalities are not determined mutually any longer.
Title Existence Condition for (0; 1)-Matrices with Given Row Sums and Certain Fixed Zeros
Speaker Wei Chen, The Hong Kong University of science and technology, China
Abstract We study the existence of (0; 1)-matrices with given row sums, given column sums, where the
ones are permitted only in a set of positions that forms a Young diagram. By translating the problem into
a flow feasibility problem and applying the max-flow min-cut theorem, an analytic necessary and sufficient
condition is obtained for the existence of such (0; 1)-matrices given in terms of the non-negativity of a tensor.
This tensor is referred to as the structure tensor since it is determined only by the row sums, column sums,
and the positions of fixed zeros. The established result is then applied to an interesting engineering problem:
the duration differentiated energy services with different deadlines.
Title Estimating Nonnegative Fiber Orientation Distribution Functions
Speaker Yannan Chen, Zhengzhou University, China
Abstract In diffusion-weighted magnetic resonance imaging, the estimation of multiplier nerve fiber bundles
in each pixel is a critical issue for exploring the connection of cerebral tissue. As a probability density function, the fiber orientation distribution function (fODF) must be nonnegative in all directions. To construct
a statistical meaningful fODF, we approximate it by a sum of squares polynomials whose coefficients are
the image of a positive semidefinite (PSD) matrix under a linear map. Duo to the sparsity of the nerve
fiber bundles in biological tissue, we employ a heuristic regularization which is the nuclear norm of the
PSD matrix. Then, we apply them in a spherical deconvolution model, and obtain the novel semidefinite
programming method for the nonnegative fODF estimation. Whereafter, to solve the semidefinite programming efficiently, we proposed a Peaceman–Rachform Splitting method, whose global and local convergence
properties are analyzed. Numerical results on synthetic data show that the novel semidefinite programming
method gives more accurate fiber orientations and volume factors estimation. In human brain study, the
contour profile of fibers constructed by the novel semidefinite programming method coincides with the results
from neuroanatomy.
19
Title Implicit Conjugate Gradient Method for Sylvester Tensor Equation
Speaker Zhen Chen, Guizhou Normal University, China
Abstract In this talk, we present an implicit conjugate gradient method for the Sylvester tensor equation
which the coefficient matrix is symmetric positive definite and the tensor on the right hand side is rank
1. The approximate solution, the conjugate direction and the residual obtained by this method process
not only the Tucker decomposition format but also simple iterative relation. Comparing with the standard
conjugate gradient method for solving the Sylvester tensor equation, the algorithm we proposed can reduce
much computational cost and memory.
Title A Feasible Trust-region Method for Calculating Extreme Z-eigenvalues of Symmetric Tensors
Speaker Chunfeng Cui, Chinese Academy of Sciences
Abstract It is known that computing the largest (smallest) Z-eigenvalue of a symmetric tensor is equivalent
to maximizing (minimizing) a homogenous polynomial over the unit sphere. Based on such a reformulation,
we shall propose a feasible trust-region method for calculating extreme Z-eigenvalues of symmetric tensors.
One basic feature of the method is that the true Hessian, which is ready for polynomials, is utilized in the
trust-region subproblem so that any cluster point of the iterations can be shown to satisfy the second-order
necessary conditions. The other feature is that after a trial step dk is provided by solving the trust-region
subproblem at the current point xk , the projection of xk + dk to the unit sphere, instead of the point
xk + dk itself, is judged and if successful, is used for the next point. Global convergence and local quadratic
convergence of the feasible trust-region method are established for the tensor Z-eigenvalue problem. The
preliminary numerical results over several testing problems show that the feasible trust-region method is
quite promising.
Title An Eigenvalue Problem for Even Order Tensors
Speaker Lubin Cui, Henan Normal University, China
Abstract In this paper, we study an eigenvalue problem for even order tensors. By using the matrix
unfolding of even order tensors, we can establishthe relationship between a tensor eigenvalue problem and a
multilevelmatrix eigenvalue problem. By considering a higher order singular value decompositionof a tensor,
we show that a higher-order singular values are the square rootof the eigenvalues of the product of the tensor
and its conjugate transpose.This result is similar to that in matrix case.Also we study an eigenvalue problem
for Toeplitz/circulant tensorswhere they have some applications in the literature.In particular, we show the
diagonalization of circulant tensors,provide the lower and upper bounds of the eigenvalues of Toeplitz tensors.
Title Fast Hankel Tensor-Vector Product and Its Application to Exponential Data Fitting
Speaker Weiyang Ding, Fudan Universiy, Shanghai, P.R.China
Abstract This talk is contributed to a fast algorithm for Hankel tensor-vector products. First we explain the
necessity of fast algorithms for Hankel and block Hankel tensor-vector products by sketching the algorithm
for both one- and multi-dimensional exponential data fitting. For proposing the fast algorithm, we define and
investigate a special class of Hankel tensors that can be diagonalized by the Fourier matrices, which is called
anti-circulant tensors. Then we obtain a fast algorithm for Hankel tensor-vector products by embedding a
Hankel tensor into a larger anti-circulant tensor. The computational complexity is about O(m2 nlogmn) for
a square Hankel tensor of order m and dimension n, and the numerical examples also show the efficiency of
this scheme. Moreover, the block version for multi-level block Hankel tensors is discussed as well.
Title Flexible global generalized Hessenberg methods for linear systems with multiple right-hand sides
Speaker Chuanqing Gu, Shanghai University, China
Abstract A variant of the global generalized Hessenberg method is presented which allows varying preconditioning at each restart. Theoretical results that relate the residual norm of this new method with its original
20
version are developed. As two special variants, the flexible global GMRES method and the flexible global
CMRH method are investigated both theoretically and experimentally. Numerical examples are conducted
to illustrate the performance of these two flexible global methods in comparison with both the original global
methods and weighted global methods.
Title A conjecture on the primitive degree of tensors
Speaker Zilong He, South China Normal University, China
Abstract In this paper, we prove: Let A be a nonnegative primitive tensor with order m and dimension n.
Then its primitive degree γ(A) ≤ (n − 1)2 + 1, and the upper bound is sharp. This confirms a conjecture of
Shao(A general product of tensors with applications, Linear Algebra and its Appl).
Title Self-adjoint Matrix Polynomial Equation: Solvability Theory, Iteration Methods and Perturbation
Analysis
Speaker Zhigang Jia, Jiangsu Normal University, China
Abstract The solvability theory of an important self-adjoint polynomial matrix equation is presented,
including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions
under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given
with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the
maximal or unique HPD solution is designed and tested by numerical experiments.
Title On the M-Rank of Even-Order Tensor and Its Applications in Low-Rank Tensor Optimization
Speaker Bo Jiang, Shanghai University of Finance and Economics
Abstract In this talk, we consider low-rank tensor optimization problems. Since computing the CP-rank
of a given tensor is NP-hard, we propose a new rank definition to even-order tensors, namely, the M-rank.
We discuss the relation between M-rank with the CP-rank and symmetric CP-rank of even-order tensor. In
particular, CP-rank and symmetric CP-rank for fourth-order tensors can be both lower and upper bounded
(up to a constant) by the corresponding M-rank. Then we study the low M-rank tensor optimization.
Numerical results on both synthetic data and real data from colored video completion and decomposition
problems are reported. The results suggest that the M-rank is an easy computable replacement and good
approximation of CP-rank in practice.
Title Norm estimates of ω-circulant operator matrices and isomorphic operators for ω-circulant algebra
Speaker Zhaolin Jiang, Linyi University, China
Abstract An n × n ω-circulant matrix which has a specific structure is a type of important matrix. Several
norm equalities and inequalities are proved for ω-circulant operator matrices with ω = eiθ (0 ≤ θ < 2π)
in this paper. We give the special cases for norm equalities and inequalities, such as the usual operator
norm and the Schatten p-norm. Pinching type inequality is also proposed for weakly unitarily invariant
norms. Meanwhile, we present that the set of ω-circulant matrices with complex entries has an idempotent
basis. Based on this basis, we introduce an automorphism on the ω-circulant algebra and then show different
operators on linear vector space that are isomorphic to the ω-circulant algebra. The function properties,
other idempotent bases and a linear involution are discussed for ω-circulant algebra. These results are closely
related to the special structure of ω-circulant matrices.
Title A note on the location of real eigenvalues of some class of tensors
Speaker Hongwei Jin, Hunan University, China
Abstract In this paper, we have a further study on B-tensors and B-tensors. We investigate the determinant
of an even order symmetry B-tensor by giving a new condition ensuring a tensor to be a B-tensors. Then,
we improve the interval of H-eigenvalues of an even order symmetric tensor obtained in Z. Chen, etc. [2014,
arXiv:1408.4634]. For some class of tensors, we show that the improved interval is contained in the interval
21
provided by the Gerschgorin disks for tensors. Furthermore, we dene two new class of tensors, called BRtensors and B0R-tensors, which contain B-tensors and B0-tensors. Some properties are studied. We see that
if an even order Z-tensor is a BR-tensor, then it is a P-tensor.
Title Research on the low rank approximations of tensors
Speaker Xu Kong, Liaocheng University, China
Abstract Low rank tensor approximations play an important role in numerical analysis and signal processing. In this talk, I will exhibit some properties about the low rank approximation (mainly the best rank-one
approximation) of a tensor, then I will present a cyclic coordinate descent method for computing the low
rank approximations. It should be noted that our method can provide an efficient way for computing the
low rank approximations of nonnegative tensors and symmetry tensors. At last of this talk, I focus my
attention on the low rank tensor approximations with sparsity constraints, and present some results relating
to the tensor completion and robust low rank tensor decompositions, which have wide applications in image
processing.
Title Some Recent Advances of Polynomial Optimization: going back and forth between the “polynomial
world” and the “convexity world”
Speaker Guoyin Li, The University of New South Wales, Australia
Abstract Optimization problems involving polynomial functions are of great importance in applied mathematics and engineering, and they are intrinsically hard problems. They arise in important engineering
applications such as the sensor network localization problem, and provide a rich and fruitful interaction between algebraic-geometric concepts and modern convex programming (semi-definite programming). In this
talk, we will discuss some recent progress of the polynomial (semi-algebraic) optimization with a focus on the
intrinsic link between the polynomial structure and the hidden convexity structure. We will describe the key
results in this new area, highlighting the geometric and conceptual aspects as well as recent work on global
optimality theory, algorithms and applications. If time allows, we will also explain how the semi-algebraic
structure helps us to analyze some important and classical algorithms in optimization such as alternating
projection algorithm, proximal point algorithm and Douglas-Rachford algorithm.
Title A new definition of geometric multiplicity of tensor eigenvalues and some results based on it
Speaker Yiyong Li, Nankai University, China
Abstract We give a new definition of geometric multiplicity for nonnegative tensors and based on this, we
study the geometric and algebraic multiplicity of irreducible tensors’ eigenvalues. We get the result that the
eigenvalues with modulus ρ(A) have the same geometric multiplicity. We also prove that two dimensional
nonnegative tensors’ geometric multiplicity of eigenvalues is equal to algebraic multiplicity of eigenvalues.
Title An effective preconditioner for the incompressive fluid problems.
Speaker Jia Liu, Univeristy of West Florida, USA
Abstract This article describes a new numerical solver for the linear system coming from the incompressible
fluid problems. The proposed solver is written in Python which is a newly developed language. The
Python packages are built to solve the Navier-Stokes equations with existing libraries. We focused on the
new preconditioned Krylov subspace iterative methods in the linearized systems. Numerical results of the
performances of the Preconditioned iterative methods are demonstrated. The comparison between Python
and Matlab is discussed at the end of the paper.
Title A fast random solver for a class of linear systems
Speaker Chen Long, National University of Defense Technology, China
Abstract A fast solver for a class of linear systems is proposed for some large scale cases. The main idea of
the algorithm is based on random method and updating inverse technique. Compared with some state-ofthe-art general algorithms, such as GMRES and Bi-CGSTAB, this solver has a much lower computational
complexity without loss of accuracy. Numerical experiments illustrate its efficiency and numerical stability.
22
Title Linear operators and positive semidefiniteness of symmetric tensor spaces
Speaker Ziyan Luo, Beijing Jiaotong University, China
Abstract We mainly focus on symmetric tensor spaces and cones arising from polynomial optimization and
physical sciences. As a start, we propose a decomposition invariance theorem for linear operators over the
symmetric tensor space, which leads to several other interesting properties in symmetric tensor spaces. We
then consider the positive semidefiniteness of linear operators which deduces the convexity of the Frobenius
norm function of a symmetric tensor. Furthermore, we characterize the symmetric positive semidefinite
tensor (SDT) cone by employing the properties of linear operators, design some face structures of its dual
cone, and analyze its relationship to many other tensor cones. In particular, we show that the cone is
self-dual if and only if the polynomial is quadratic, give specific characterizations of tensors that are in the
primal cone but not in the dual for higher order cases, and develop a complete relationship map among the
tensor cones appeared in the literature.
Title The positive definite solution to a nonlinear matrix equation
Speaker Jie Meng, Pusan National University , Korea
Abstract In this talk, the nonlinear matrix equation F (X) = X p + AXAQ = 0 is studied, where p is a
positive integer, A is a nonsingular n · n complex matrix and Q is a n · n positive definite matrix. We show
that the equation has a unique Hermitian positive definite solution by using fixed-point iteration. A double
of elegant estimates of the positive definite solution are obtained. Three iterative methods for obtaining
the positive definite solution are presented. Finally, numerical experiments to illustrate the behavior of the
considered algorithms are given.
Title Tensor representations of geometric measures of quantum entanglement
Speaker Guyan Ni, National University of Defense Technology, Changsha, China
Abstract The quantum entanglement measure plays an important role in the quantum information theory.
There are several different definitions of the geometric measure of entanglement have been introduced and
studied in literatures. However, geometric measures of entanglement problems are multilinear optimization
problems. Hence, in this paper, geometric measures of quantum entanglement are represented by optimizations of tensors, and relations of different definitions of the geometric measure are obtained by mathematical
methods.
Title Quasi-Newton method for computing Z-eigenpairs of a real symmetric tensor
Speaker Qin Ni, Nanjing University of Aeronautics and Astronautics
Abstract In this talk, we propose a quasi-Newton method for computing Z-eigenpairs of a real symmetric
tensor. The iterative sequence generated by the quasi-Newton method is norm descent for the function
corresponding to the eigenvalue equations. On the basis of the special structure of the system of eigenvalue
equations, we can obtain a descent direction by solving a system of linear equations every iteration. The
global and superlinear convergence of the proposed method are established. The numerical results show that
this method is promising.
Title On some new stable classes of P -matrices
Speaker Volha Kushel, Shanghai Jiao Tong University, China
Abstract In this talk, we consider spectral properties of P 2 -matrices and weakly sign-symmetric P -matrices
(so called GKK-matrices), in connection with some open problems of matrix theory. We study the relations
between these two classes of matrices and analyze the conditions of their positive stability. We also study
the properties of positive scalings of matrices from this two classes. Applying the obtained scheme, we prove
positive stability of some new classes of P -matrices.
23
Title The existence and convergence of two iterations for differentiable order-convex matrix functions
Speaker Sang-Hyup, Pusan National University, Korea
Abstract In stochastic problems and some physical problems, it is important that finding the elementwise
minimal nonnegative or nonpositive solvent of a nonlinear matrix equation. A lot of such equations introduced
in several papers are differentiable order-convex functions. We will show the existence of a solution of these
equations which are like nonsymmetric algebraic Riccati equations, guadratic matrix equations, and matrix
polynomials. Using the properties of differentiable order-convex functions, we will show that the fixed point
iterations and the Newton iterations of the equations are well-defined and converge to a special solution.
Finally, it is given numerical experiments of the iterations for the equations.
Title Some results in extremal spectral hypergraph theory
Speaker Jiayu Shao Tongji University, China
Abstract In this talk, we show that the adjacency tensor, Laplacian tensor and signless Laplacian tensor
of a uniform directed hypergraph each has n linearly independent H-eigenvectors. Some lower and upper
bounds for the largest and smallest adjacency, Laplacian and signless Laplacian H-eigenvalues of a uniform
directed hypergraph are given. For a uniform directed hypergraph, the smallest Laplacian H-eigenvalue is
0. For a uniform directed hypergraph, the upper bound of the largest adjacency and signless Laplacian
H-eigenvalues are achieved if and only if it is a complete directed hypergraph. At the same time, we propose
some conjectures about the nonnegativity of one H-eigenvector corresponding to the largest H-eigenvalue,
and some questions about whether the Laplacian and signless Laplacian tensors are positive semi-definite
for a uniform directed hypergraph.
Title Properties of Some Classes of Structured Tensors
Speaker Yisheng Song, Henan Normal University, China
Abstract The concept of several classes of special structured matrices (P matrices) to higher order tensors.
Their relationships with positive semi-definite tensors and some other structured tensors are discussed . We
show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same
class, with a lower dimension. The potential links of such structured tensors with optimization, nonlinear
equations, nonlinear complementarity problems, variational inequalities and the nonnegative tensor theory
are also discussed.
Title Some results on the generalized inverse of tensors and idempotent tensors
Speaker Lizhu Sun, Harbin Institute of Technology, China
Abstract Let A be an order t dimension m × n × · · · × n tensor over complex field. In this paper, we study
some generalized inverses of A, the k-T-idempotent tensors and the idempotent tensors based on the general
tensor product. Using the tensor generalized inverse, some solutions of the equation A · xt−1 = b are given,
where x and b are dimension n and m vectors, respectively. The generalized inverses of some block tensors,
the eigenvalues of k-T-idempotent tensors and idempotent tensors are given. And the relation between the
generalized inverses of tensors and the k-T-idempotent tensors is also showed.
Title Analysis of The Structured Perturbation for the Left Circulant Linear System
Speaker Xia Tang, Linyi University, China
Abstract In this paper, based on the eigenvalues and the style spectral decomposition of the left circulant
matrix, the structured perturbation analysis is studied, which included the condition number and the upper
bound of the relative error. And then, the optimal backward perturbation is discussed. Simultaneously, the
algorithm for the optimal backward perturbation bound is given. Finally, a numerical example is provided
to verify the effectiveness of the algorithm.
Title The Chebyshev Skew Circulant Type Matrices With Polynomials
Speaker Jianyong Wang, Linyi University, China
24
Abstract In this paper,We consider the skew circulant matrices with Chebyshev polynomials. Firstly, we
discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices
by constructing the transformation matrices. Finally, we obtain the Smith normal forms of skew circulant
matrices with Chebyshev polynomials,where including the four kinds Chebyshev polynomials.
Title Are There Sixth Order Three Dimensional PNS Hankel Tensors?
Speaker Qun Wang, The Hong Kong Polytechnic University, China
Abstract Are there positive semi-definite (PSD) non-SOS Hankel tensors? If the answer to this question is
no, then the problem for determining an even order Hankel tensor is PSD or not is solvable in polynomialtime. By Hilbert, one of the cases of low order (degree) and dimension (number of variables), in which there
are PSD non-SOS (PNS) symmetric tensors (homogeneous polynomials), is of order six and dimension three.
The famous Motzkin polynomial is of degree six with three variables. In this paper, we study the existence
problem of sixth order three dimensional PNS Hankel tensors. We study several special cases of sixth order
three dimensional Hankel tensors. No PNS Hankel tensors are found in these cases. We then randomly
generate several thousands of sixth order three dimensional Hankel tensors and make them PSD by adding
adequate multiple of a fixed sixth order three dimensional positive definite Hankel tensors. Again, still no
PNS Hankel tensors are found. Thus, we make a conjecture that there are no sixth order three dimensional
PNS Hankel tensors. This implies that the problem for determining a given sixth order three dimensional
Hankel tensor is PSD or not can be solved by a semi-definite linear programming problem.
Title Nonsingular H-Tensors and Their Criteria
Speaker Yiju Wang, Qufu Normal University, China
Abstract An H-tensor is a new developed concept in tensor analysis and it is an extension of an H-matrix
and an M-tensor. Based on the spectral theory of nonnegative tensors, several equivalent conditions of
nonsingular H-tensors are established in the literature. However, these conditions are not appropriate to be
used as criteria in identifying nonsingular H-tensors as they are hard to verify. In this paper, based on the
diagonal product dominance and S diagonal product dominance of a tensor, we establish some implementable
criteria in identifying nonsingular H-tensors. The positive definiteness of nonsingular H-tensors with positive
diagonal entries is also obtained in this paper. The results obtained in this paper extend the corresponding
conclusions for nonsingular H-matrices and improve the existing results for nonsingular H-tensors.
Title Von Neumanns trace inequality for tensors
Speaker Tianwen Wei, Universite de Franche-Comte
Abstract In this contribution we generalize von Neumanns trace inequality to cope with tensors. Our work
is based on de Lathauwers well-known result (A multilinear singular value decomposition, SIAM J. Matrix.
Anal. Appl., 2000) of higher order singular value decomposition (HOSVD). We show that an extended
version of the classical von Neumanns inequality holds for tensors. We prove that the inequality becomes
an equality if and only if there exists an orthonormal basis for each mode of the involved tensors such that
under these basis the two tensors are block-wise diagonal and the corresponding blocks are equal up to a
constant multiple. Several consequences are discussed and examples are given. Our result may be applied
to characterize the subdifferential of certain tensor norms and hopefully give insight into solving tensor
completion problems.
Title Spectral directed hypergraph theory via tensor
Speaker Jinshan Xie, Longyan University, China
Abstract In this talk, we show that the adjacency tensor, Laplacian tensor and signless Laplacian tensor
of a uniform directed hypergraph each has n linearly independent H-eigenvectors. Some lower and upper
bounds for the largest and smallest adjacency, Laplacian and signless Laplacian H-eigenvalues of a uniform
directed hypergraph are given. For a uniform directed hypergraph, the smallest Laplacian H-eigenvalue is
0. For a uniform directed hypergraph, the upper bound of the largest adjacency and signless Laplacian
25
H-eigenvalues are achieved if and only if it is a complete directed hypergraph. At the same time, we propose
some conjectures about the nonnegativity of one H-eigenvector corresponding to the largest H-eigenvalue,
and some questions about whether the Laplacian and signless Laplacian tensors are positive semi-definite
for a uniform directed hypergraph.
Title The Determinants, Inverses of Gaussian Fibonacci ω-Circulant and Left ω-Circulant Matrices
Speaker Hongxia Xing, Linyi University, China
Abstract Let Aω,r,n be a Gaussian Fibonacci ω-circulant matrix and A0ω,r,n be a Gaussian Fibonacci left ωcirculant matrix, and both of the first rows are (Gr+1 , Gr+2 , ..., Gr+n ), where Gr+n is the (r + n)th Gaussian
Fibonacci number, r is a nonnegative integer and ω ∈ C. In this paper, by constructing the transformation
matrices, the explicit determinants of A and A0 are expressed. Moreover, we discuss the singularities of these
matrices and the inverse matrices of them are obtained.
Title On Skew Circulant Type Matrices Involving any Continuous Pell Numbers
Speaker Jinjiang Yao, Linyi University, China
Abstract Circulant and skew circulant matrices have become an important tool in networks engineering. In
this paper, we consider the skew circulant and skew left circulant matrices with any continuous Pell numbers.
we discuss the invertibility of the skew circulant matrix and present the determinants and the inverse matrix
by constructing the transformation matrices. We obtain the determinants and the inverse matrices of the
skew left circulant matrices by utilizing the relation between skew left circulant matrices and skew circulant
matrix, respectively. Finaly, the four kinds of norms and bounds for the spread of these matrices are given,
respectively.
Title Improved tensor decomposition for spectroscopy analysis
Speaker Shaohui Yu, Hefei Normal University, China
Abstract With the development of hyphenated instruments, higher demands of tensor decomposition are
proposed for the more data. Third-order tensor is the mainstream in spectroscopy analysis. However, some
second-order calibration methods dont work well that is affected by the redundancy and multi-collinearity
of third-order tensor. Based on the structure characteristic of third-order tensor, an improved methods for
third-order spectral tensor is proposed.
Title The largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths
Speaker Junjie Yue, Tsinghua University
Abstract We investigate the H-spectra of k-uniform loose paths and loose cycles. We show that all Heigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are real roots of
several equations. The numerical results shows that all H-spectra with respect to k for the k-uniform loose
paths and loose cycles are convergent when their length are fixed. Especially, we show that the convergence
of H-spectra of loose paths with length being 3 and loose paths with length being 2 are all right. The rest
is a conjecture to be presented here for future research.
Title On equally absolute sum matrices/tensors
Speaker Chengyi Zhang, Xi‘an Polytechnic University, China
Abstract In this talk, the equally absolute sum matrix/tensor is proposed to study the relationship between
spectral radius and some norms of a nonnegative matrix/tensor. Above all, some necessary and sufficient
conditions such that spectral radius of a nonnegative matrix is equal to its some norms such as spectral
norm, 1-norm and -norm are proposed to give further some new bounds on spectral radius and spectral
norm of a matrix. Based on the results above, the relationship between spectral radius and some norms
of a nonnegative tensor are studied. Some norms of a high tensor are defined and summarized to present
some properties. Then some necessary and sufficient conditions are proposed such that spectral radius of
a nonnegative tensor is equal to its some norms such as spectral norm, 1-norm of mode-k and -norm of
26
mode-k. Finally, based on the results of Ledermann (1950), Taussky (1951), Ostrowski (1952,1960), Hall
and Porsching(1969) and Brauer (1956,1957,1974), some new bounds on spectral radius and spectral norm
of a nonnegative tensor are presented.
Title Tensor Completion via Iterative Hard Thresholding
Speaker Min Zhang, Tianjin University, China
Abstract Tensor completion has many applications in computer vision and graphics such as image inpainting
and video inpainting. In this paper, we propose an iterative hard thresholding algorithm with giving the
upper bound of the n-rank in advance. The convergence analysis of the proposed algorithm is also presented.
Particularly, we show that for the noiseless case, the linear convergence with rate 1/2 can be obtained for the
proposed algorithm under proper conditions. Additionally, combining an effective heuristic for determining
n-rank, we can also apply the proposed algorithm to solve tensor completion when n-rank is unknown in
advance. Some preliminary numerical results on randomly generated and real low n-rank tensor completion
problems are reported, which show the efficiency of the proposed algorithms.
Title Counting extreme U1 matrices and characterizing the quadratic doubly stochastic operators
Speaker Quanbing Zhang, Anhui University, China
Abstract U1 matrices and extreme U1 matrices are successfully used to study quadratic doubly stochastic
operators in R. Ganikhodzhaev and F. Shahidi’s paper: ”Doubly stochastic quadratic operators and Birkhoff’s problem”(Linear Algebra and Appl.,432(2010)24-35) where a necessary condition for a U1 matrix to be
extreme is given. In the paper: ”On extreme U1 matrices”(Linear Algebra and Appl.,438(2013)3905-3912)
Yang and Xu give a necessary and sufficient condition for a symmetric nonnegative matrix to be an extreme
U1 matrix and investigate the structure of extreme U1 matrices. In this paper we count the number of
the permutation equivalence classes of the n × n extreme U1 matrices and characterize the structure of the
quadratic stochastic operators and the quadratic doubly stochastic operators.
Title The algebraic connectivity of graphs
Speaker Xiaodong Zhang, Shanghai Jiao Tong University, China
Abstract Let G be a simple graph of order n and L(G) = D(G)−A(G) be its Laplacian matrix, where D(G)
and A(G) are the degree diagonal and adjacency matrices, respectively. The the second smallest eigenvalue
of L(G) is called the algebraic connectivity of G. In this talk, we survey some new results and progress on
the algebraic connectivity. In particular, we present some relationships between the algebraic connectivity
and the graph parameters, such as the clique number, the matching number, the independence number,the
isoperimetric number, etc. Moreover, the algebraic connectivity of random graphs will be included.
Title A Corrected Procedure for Tensor Completion
Speaker Xiongjun Zhang, Hunan University, China
Abstract In this talk, we present the low rank approximation problem on recovery of a low-rank multilinear
data under limited sampling. Many convex relaxation methods for this problem are based on nuclear norm
of matrix. However, the nuclear norm minimization may fail to produce a low-rank solution of the matrix.
In order to get a recovery with low rank and high accuracy, we apply rank-corrected method for matrix
completion to tensor completion and propose a two-stage method for tensor completion. The first stage
is used to generate a preestimator by solving a square deal convex model. The second stage is a rankcorrect procedure to generate an low-rank and high-accuracy recovery with the pre-estimator. We construct
alternating direction method of multipliers (ADMM) to solve the convex problems. Numerical results are
reported to validate the efficiency of our proposed rank-corrected procedure.
Title Computing MP pseudo inverses of polynomial matrices
Speaker Yang Zhang, University of Manitoba, Canada
Abstract Matrices with non commutative entries has a long research history, at least dated back to Ja-
27
cobson’s seminal work in 1940s. In past ten years, these matrices have attracted more and more people in
computer algebra area, and many important properties have been discussed by using symbolic computation
methods, for example, various fast algorithms for computing Hermite forms and Smith forms for Ore matrices. In this paper, we consider Moore-Penrose pseudo inverse of Ore matrices and quaternion polynomial
matrices. It is well-known that every matrix over a field has a MP pseudo inverse. But it is not true for Ore
matrices in general. At first, we use blocked matrices and GCD computations to give some sufficient and
necessary conditions for Ore matrices to have MP pseudo inverses. Then when MP pseudo inverses exist,
we develop algorithms to compute them. All algorithms are implemented in the symbolic programming
language Maple, and tested on examples.
Title Resistance distance and resistance matrix of a graph
Speaker Jiang Zhou, Harbin Engineering University
Abstract Resistance distance is a distance function on graphs. In this talk, we report some basic properties
of the resistance distance, kirchhoff index and resistance matrix of a graph.
28
No.
Name
Affiliate
Addr
Email
1
ABDUR
Shanghai University
China
[email protected]
2
Andrzej Cichocki
Brain Science Institute
Japan
[email protected]
3
Bai Minru(白敏茹)
Hunan University
China
[email protected]
4
Bai Zhaojun
University of California,Davis
USA
[email protected]
5
Bian Hong(边红)
Xinjiang Normal University
China
[email protected]
6
Bu Changjiang(卜长江)
Harbin Institute of Technology
China
[email protected]
7
Cao Chongguang(曹重光)
Heilongjiang University
China
[email protected]
8
Chang An(常安)
Fuzhou University
China
[email protected]
9
Che Maolin
Fudan University
China
[email protected]
10
Chen Haibin
The Hong Kong Polytechnic University
Hong Kong
[email protected]
11
Chen Hong(陈虹)
The PLA Information Engineering University
China
12
Chen Ling(陈铃)
13
Chen Meixiang(陈梅香)
14
Chen Wei
15
Chen Xiaohong(陈晓红)
16
Guizhou Normal University、Shandong Jianzhu
China
[email protected]
China
[email protected]
Hong Kong
[email protected]
Hubei Normal University
China
[email protected]
Chen Yannan(陈艳男)
Zhengzhou University
China
[email protected]
17
Chen Yihui(陈溢晖)
Tianjin University
China
[email protected]
18
Chen Yinlan(陈引兰)
Hubei Normal University
China
[email protected]
19
Chen Zhen(陈震)
China
[email protected]
20
Chen Zhongming
China
[email protected]
21
Cheng Guanghui(程光辉)
China
[email protected]
22
Chenjianlong(陈建龙)
Southeast University
China
[email protected]
23
Chi-Kwong Li
College of William and Marry
USA
[email protected]
24
Cui Chunfeng(崔春风)
Chinese Academy of Sciences
China
[email protected]
25
Cui Lubin(崔鲁宾)
Henan Normal University
China
[email protected]
26
Dai Ping'an(戴平凡)
Sanming University
China
[email protected]
27
Dai Yuhong(戴彧虹)
Chinese Academy of Sciences
China
[email protected]
28
Deng Yuanbei(邓远北)
Hunan University
China
[email protected]
29
Ding Weiyang(丁维扬)
Fudan University
China
[email protected]
30
Dong Yinghui(董迎辉)
Suzhou University of Sience and Technology
China
[email protected]
31
Du Dagang(杜大刚)
Suzhou University of Sience and Technology
China
[email protected]
32
Edinah K Gnang
Princeton University
USA
[email protected]
33
Eugene Tyrtyshnikov
Russian Academy of Sciences
Russia
[email protected]
34
Fan Yizheng(范益政)
Anhui University
China
[email protected]
35
Fang Kunfu(方坤夫)
Huzhou University
China
[email protected]
36
Fang Xiaowei(方晓伟)
China
[email protected]
37
Fu Qin(傅勤)
China
[email protected]
University
Putian University
The Hong Kong University of Science and
Technology
Guizhou Normal University、Beijing
Computational Science Research Center
Nankai University
University of Electronic Science and
Technology of China
Nanjing University of Aeronautics and
Astronautics
Suzhou University of Sience and Technology
29
38
Gao Yubin(高玉斌)
North University of China
China
[email protected]
39
Gu Chuanqing(顾传青)
Shanghai University
China
[email protected]
40
Gu Jiansheng(谷建胜)
Suzhou University of Sience and Technology
China
[email protected]
41
Guan Jinrui(关晋瑞)
Amoy University
China
[email protected]
42
Guo Wenbin(郭文彬)
Liaocheng University
China
[email protected]
43
He Lifang(何丽芳)
Guangdong University of Technology
China
[email protected]
44
He Zilong(何子龙)
South China Normal University
China
[email protected]
45
Hua Bing(滑冰)
National University of Defense Technology
China
[email protected]
46
Huang Shaowu(黄少武)
Shanghai University
China
[email protected]
47
Huang Zhenghai(黄正海)
Tianjin University
China
[email protected]
48
Ji Yin(吉颖)
Tianjin University
China
[email protected]
49
Jia Lixin(贾利新)
The PLA Information Engineering University
China
[email protected]
50
Jia Zhigang(贾志刚)
Jiangsu Normal University
China
[email protected]
51
Jiang Bo(江波)
Shanghai University of Finance and Economics
China
[email protected]
52
Jiang Erxiong(蒋尔雄)
Shanghai University
China
[email protected]
53
Jiang Zhaolin(江兆林)
Linyi University
China
[email protected]
54
Jie Meng
Pusan National University
Korean
[email protected]
55
Jin Hongwei(靳宏伟)
Hunan University
China
[email protected]
56
Jiu Ding
University of Southern Mississippi
USA
[email protected]
57
Jorge Delgado Gracia
Univ. de Zaragoza
Spanish
[email protected]
58
Joshua Cooper
University of South Carolina
USA
[email protected]
59
Juan Manuel Pena
Universidad de Zaragoza
Spain
[email protected]
60
Junjun
Amoy University
China
[email protected]
61
Lars Elden
Linkoping University
Sweden
[email protected]
62
Lek-Heng Lim
Univ. of Chicago
USA
[email protected]
63
Li Guoyin
University of New South Wales
Australia
[email protected]
64
Li Guozhong(李国重)
The PLA Information Engineering University
China
65
Li haiyang(李海洋)
Xi`an Polytechnic University
China
66
Li Jicheng(李继成)
Xi'an Jiaotong University
China
[email protected]
67
Li Lei(李磊)
Shanghai University
China
[email protected]
68
Li Shujie(李姝洁)
Amoy University
China
[email protected]
69
Li Tao(李涛)
Suzhou University of Sience and Technology
China
[email protected]
70
Li Wei(李薇)
Fuzhou University
China
[email protected]
71
Li Wen(黎稳)
South China Normal University
China
[email protected]
72
Li Yaotang(李耀堂)
Yunnan University
China
[email protected]
73
Li Ying(李莹)
Liaocheng University
China
[email protected]
74
Li Yiyong(李益永)
Nankai University
China
[email protected]
75
Li Yuanyuan(李媛媛)
Jianghan University
China
[email protected]
76
Liang Maolin(梁茂林)
Lanzhou University
China
[email protected]
77
Lieven De Lathauwer
University of Leuven
Belgium
78
Ling Chen(凌晨)
Hangzhou Dianzi University
China
[email protected]
79
Liu Aijing(刘爱晶)
Qufu Normal University
China
[email protected]
30
[email protected]
80
Liu jia(刘嘉)
University of West Florida
USA
[email protected]
81
Liu Lixia(刘丽霞)
Xidian University
China
[email protected]
82
Liu Qilong(刘奇龙)
Yunnan University
China
[email protected]
83
Liu Qingbing(刘庆兵)
Zhejiang Wanli University
China
[email protected]
84
Liu xiaoji(刘晓冀)
GuangXi University for Nationalities
China
[email protected]
85
Liu Yingliang(刘颖良)
Dalian University of Technology
China
[email protected]
86
Long Chen(龙忱)
National University of Defense Technology
China
[email protected]
87
Lu Junxiang(卢俊香)
Xi'an Polytechnic University
China
88
Lu Shannian(陆珊年)
Higher Education Press
China
[email protected]
89
Luke Oeding
Auburn Univ.
USA
[email protected]
90
Luo Gaojun(罗高骏)
Hubei Normal University
China
[email protected]
91
Luo Ziyan(罗自炎)
Beijing Jiaotong University
China
[email protected]
92
Miao Zhengke(苗正科)
Jiangsu Normal University
China
[email protected]
93
Michael Ng.
Hong Kong Baptist University
Hong Kong
[email protected]
94
Naomi Shaked-Monderer
The Max Stern Yezreel Valley College,Israel
Israel
[email protected]
95
Ni Guyan(倪谷炎)
National University of Defense Technology
China
[email protected]
96
Ni Qin(倪勤)
China
[email protected]
97
Pan Junjun(潘珺珺)
China
[email protected]
98
Peng Hua(彭华)
China
[email protected]
99
Peter Semrl
University of Ljubljana
Slovenia
[email protected]
100
Qi Liqun(祁力群)
The Hong Kong Polytechnic University
Hong Kong
[email protected]
101
Ren Haizhen(任海珍)
Qinghai Normal University
China
[email protected]
102
Sang Caili(桑彩丽)
Guizhou Minzu University
China
[email protected]
103
Sang-hyup Seo
Pusan National University
Korean
[email protected]
104
Sanzheng Qiao
University of Mcmaster
Canada
[email protected]
105
Shao Jiayu(邵嘉裕)
Tongji University
China
[email protected]
106
Shao Rongxia(邵荣侠)
Amoy University
China
[email protected]
107
Shao Yanling(邵燕灵)
North University of China
China
[email protected]
108
Sheng Xinping(盛兴平)
Fuyang Teachers College
China
[email protected]
109
Song Yisheng(宋义生)
Henan Normal University
China
[email protected]
110
Song Yongzhong(宋永忠)
Nanjing Normal University
China
111
Sun Lizhu(孙丽珠)
Harbin Institute of Technology
China
[email protected]
112
Sun Wenyu(孙文瑜)
Nanjing Normal University
China
[email protected]
113
Tang xia(唐霞)
Linyi University
China
114
Tang Zikai(汤自凯)
Hunan Normal University
China
[email protected]
115
Tian Guixian(田贵贤)
Zhejiang Normal University
China
[email protected]
116
Volha Kushel
Shanghai Jiao Tong University
China
[email protected]
117
Wang Feng(王峰)
Guizhou Minzu University
China
[email protected]
118
Wang Jianyong(王建勇)
Linyi University
China
[email protected]
119
Wang Kaiyong(王开永)
Suzhou University of Sience and Technology
China
[email protected]
120
Wang Qingwen(王卿文)
Shanghai University
China
[email protected]
Nanjing University of Aeronautics and
Astronautics
Amoy University
Zhengzhou Institute of Information Science and
Technology
31
121
Wang Qun(王群)
The Hong Kong Polytechnic University
Hong Kong
122
Wang Teng(王滕)
Amoy University
China
123
Wang Xiuyu(王秀玉)
Changchun University of Technology
China
[email protected]
124
Wang Yi(汪毅)
Anhui University
China
[email protected]
125
Wang Yiju(王宜举)
Qufu Normal University
China
[email protected]
126
Wang Zhongwen(汪仲文)
Kashi Normal University
China
[email protected]
127
Wei Musheng(魏木生)
Liaocheng University
China
[email protected]
128
Wei Tianwen
Universite de Franche-Comte
France
[email protected]
129
Wei Yimin(魏益民)
Fudan University
China
[email protected]
130
Wu Jianrong(吴健荣)
Suzhou University of Sience and Technology
China
[email protected]
131
Wu Shiliang(吴世良)
Anyang Normal University
China
[email protected]
132
Xia Fuquan(夏福全)
Bengbu University
China
[email protected]
133
Xie Huiqing(解惠青)
China
[email protected]
134
Xie Jinshan(谢锦山)
Longyan University
China
[email protected]
135
Xing Hongxia(邢红霞)
Linyi University
China
136
Xu Changqing(徐常青)
Suzhou University of Sience and Technology
China
[email protected]
137
Xu Kong
Liaocheng University
China
[email protected]
138
Xu Tingting(徐婷婷)
Linyi University
China
[email protected]
139
Yan Min(燕敏)
Hubei Normal University
China
[email protected]
140
Yang Hongxing(杨红杏)
Beijing University of Technology
China
[email protected]
141
Yang Qingzhi(杨庆之)
Nankai University
China
[email protected]
142
Yang Shangjun(杨尚俊)
Anhui University
China
[email protected]
143
Yang Weiwei(杨维维)
China
[email protected]
144
Yang Xiaoying(杨孝英)
Changchun University of Technology
China
[email protected]
145
Yang Zhang
University of Manitoba
Canada
[email protected]
146
Yang Zhixia(杨志霞)
Xinjiang University
China
[email protected]
147
Yao Hongmei(姚红梅)
Harbin Engineering University
China
[email protected]
148
Yao Jinjiang(姚金江)
Linyi University
China
[email protected]
149
YeonJi
Pusan National University
Korean
[email protected]
150
You lihua(尤利华)
South China Normal University
China
[email protected]
151
Yu Shaohui(于绍慧)
Hefei Normal University
China
[email protected]
152
Yuan Pingzhi(袁平之)
South China Normal University
China
[email protected]
153
Yuan Yongxin(袁永新)
Hubei Normal University
China
[email protected]
154
Yue Junjie(岳俊杰)
Tsinghua University
China
[email protected]
155
Zeng Meilan(曾梅兰)
China
[email protected]
China
[email protected]
East China University of Science and
Technology
Nanjing University of Aeronautics and
Astronautics
Nanjing University of Aeronautics and
Astronautics
[email protected]
Institute of Quantitative&Technical
156
Zeng Zili(曾力生)
Economics(IQTE),Chinese Academy of Social
Sciences(CASS)
157
Zhai Yaping(翟亚平)
Amoy University
China
[email protected]
158
Zhang Chengyi(张成毅)
Xi`an Polytechnic University
China
[email protected]
32
159
Zhang Fengxia(张凤霞)
Liaocheng University
China
[email protected]
160
Zhang Gongqing(张恭庆)
Peking University
China
[email protected]
161
Zhang Juli(张居丽)
Shanghai University
China
162
Zhang Liping(张立平)
Tsinghua University
China
[email protected]
163
Zhang Min(张敏)
Tianjin University
China
[email protected]
164
Zhang Quanbin(章权兵)
Anhui University
China
[email protected]
165
zhang weimin(张纬民)
Jiaying University
China
[email protected]
166
Zhang Xiongjun(张雄军)
Tsinghua University
China
[email protected]
167
Zhang Zhengyue(张振跃)
Zhejiang University
China
[email protected]
168
Zhao Haixing(赵海兴)
Qinghai Normal University
China
[email protected]
169
Zhao Jianli(赵建立)
Liaocheng University
China
[email protected]
170
Zhao Jianxing(赵建兴)
Guizhou Minzu University
China
[email protected]
171
Zhao Linlin(赵琳琳)
Dezhou University
China
[email protected]
172
Zhao Zhanhui(赵展辉)
Guangxi University of Science and Technology
China
[email protected]
174
Zheng Baodong(郑宝东)
Harbin Institute of Technology
China
[email protected]
175
Zheng Yutao(郑燏涛)
Lanzhou University
China
[email protected]
176
Zhou Guanglu
Curtin University
Australia
[email protected]
177
Zhou Jiang(周江)
Harbin Institute of Technology
China
[email protected]
178
Zhou Zhongcheng(周中成)
Suzhou University of Sience and Technology
China
[email protected]
179
Zhu Jianqing(朱建青)
Suzhou University of Sience and Technology
China
[email protected]
180
Zubair Ahmed
Amoy University
China
[email protected]
181
Zuo Kezheng(左可正)
Hubei Normal University
China
[email protected]
182
Raymond Nung-Sing Sze
The Hong Kong Polytechnic University
China
[email protected]
33