2016 June SHU Matrix Program Plenary - june6 - final 1cklixx.people.wm.edu/mime2016program.pdf ·...

2016 Shanghai International Workshop on

Matrix Inequalities and Matrix Equations

2016 上海矩阵不等式及矩阵方程国际会议

Shanghai University

Shanghai, China

June 8-10, 2016

Organized by Department of Mathematics, Shanghai University, Shanghai, China

Sponsored by Gaoyuan Discipline of Shanghai – Mathematics The First-class Shanghai Discipline – Mathematics

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2016 Shanghai International Workshop on

Matrix Inequalities and Matrix Equations

(MIME 2016)

Aim: The purpose of the workshop is to stimulate research and foster interaction of researchers interested in matrix inequalities, matrix equations, and their applications.

Host: Department of Mathematics, Shanghai University

Sponsors:

Gaoyuan Discipline of Shanghai – Mathematics (上海市高原学科–数学)

The First-class Shanghai Discipline – Mathematics (上海市一流学科–数学)

Organizing Committee Members: Delin Chu, National University of Singapore, Singapore

Chi-Kwong Li (Chair), College of William and Mary, USA

Tin-Yau Tam, Auburn University, USA

Qing-Wen Wang, Shanghai University, China

Fuzhen Zhang, Nova Southeastern University, USA

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Invited Speakers (28)

Jianlong Chen Southeast University

Man-Duen Choi University of Toronto, Canada

Hwa-Long Gau National Central University, Taiwan

Tongsong Jiang Heze University

Seung-Hyeok Kye Seoul National University, Korea

Aihua Li Montclair State University, USA

Chi-Kwong Li College of William and Mary, Shanghai University

Ren-Cang Li University of Texas at Arlington, USA

Ming Liao Auburn University, USA

Minghua Lin Shanghai University

Jianzhen Liu Auburn University, USA

Jianzhou Liu Xiangtan University

Yiu-Tung Poon Iowa State University, USA

Raymond Nung-Sing Sze The Hong Kong Polytechnic University, Hong Kong

Tin-Yau Tam Auburn University, USA

Jiyuan Tao Loyola University Maryland, USA

Yimin Wei Fudan University

Rui-Ping Wen Taiyuan Normal University

Ngai-Ching Wong National Sun Yat-sen University, Taiwan

Peiyuan Wu National Chiao Tung University, Taiwan

Qingxiang Xu Shanghai Normal University

Jungong Xue Fudan University

Takeaki Yamazaki Toyo University, Japan

Junfeng Yin Tongji University

Xingzhi Zhan East China Normal University

Fuzhen Zhang Nova Southeastern University, USA

Xiaodong Zhang Shanghai Jiao Tong University

Yang Zhang University of Manitoba, Canada

Conference Agenda

June 8 9:00 - 21:00

Registration at the Lobby of New Lehu Hotel

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June 9 -10 Talks

Accommodation:

New Lehu Hotel, Shanghai University, 716 Jinqiu Road

上海市宝山区锦秋路 716 号上海大学北大门乐乎新楼� � Transportation:

Pudong Airport to Shanghai University (Baoshan Campus) 1. By Metro: Pudong airport by Metro Line 2 to Jing'an Temple, change to Metro Line 7 to

Shanghai University.

2. By Taxi: Directly take taxi to 716 Jingqiu Road, Shanghai University (Baoshan Campus,

North Gate).

Hongqiao Airport to Shanghai University (Baoshan Campus)

1. By Metro: Hongqiao airport by Metro Line 2 to Jing'an Temple exchange to Metro Line 7

to Shanghai University.


North Gate).

Shanghai South Railway Station to Shanghai University (Baoshan Campus)

1. By Metro: Line 1 to Changshu Road exchange to Metro Line 7 to Shanghai University

Baoshan Campus).


North Gate).

Shanghai Railway Station to Shanghai University (Baoshan Campus)

1. By Metro: Line 1 to Changshu Road exchange to Metro Line 7 to Shanghai University

(Baoshan Campus).

2. By Metro: Line 3 to Zhenping Road exchange to Metro Line 7 to Shanghai University

(Baoshan Campus).


North Gate).

4. By Bus: Route 58: Railway Station (Hengfeng Road) -> terminus (near 716 Jingqiu Road,

Shanghai University, Baoshan Campus, North Gate).

Contact:

Dr. Minghua Lin, [email protected]

Dr. Jiancai Sun, [email protected]

Prof. Qing-Wen Wang, [email protected]

Tel: +86-21-66134715(O); +86-13162033063(M)

Fax: 86-21-66133292

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Website: http://math.shu.edu.cn/MIME2016/

Program

June 8, 2016 (Wednesday)

Time Lobby of Lehu Hotel (乐乎新楼 1 号楼大厅)

9:00-21:00 Registration

17:30-19:30 Dinner

June 9, 2016 (Thursday)

Time Xuehai Hall (学海厅)—乐乎新楼 2 号楼二楼

Speaker & Title Chair

08:15-08:45

Opening Ceremony

1. Opening remarks by Prof. Man-Duen Choi 2. Opening remarks by Prof. Chi-Kwong Li 3. Opening remarks by the leader of SHU

Qing-Wen

Wang

08:45-09:00 Group Photo

09:00-09:30 Man-Duen Choi [p.8]

Non-linear inequalities for positive linear maps Fuzhen

Zhang

09:30-10:00 Chi-Kwong Li [p.10]

Linear and non-linear matrix inequalities

10:00-10:15 Coffee/Tea Break

June 9, 2016 (Thursday)

(25 min talk + 5 min Q&A)



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10:15-10:45 Pei Yuan Wu [p.15]

Companion Matrices: Numerical Range, Crawford Number

and Zero-dilation Index

Tin-Yau

Tam

10:45-11:15 Yiu-Tung Poon [p.13]

One horse racing story, two card games,

and three matrix theorems

11:15-11:45 Ming Liao [p.11]

Convergence of products of independent random matrices

11:45-12:15 Fuzhen Zhang [p.17]

Are these permanent conjectures becoming permanent?

-- An update on a few conjectures on permanent

12:15-13:00 Lunch

Parallel Sessions

Session 1



13:30-14:00

Seung-Hyeok Kye [p.10]

Three qubit separability criteria with diagonal

and anti-diagonal entries

Chi-Kwong

Li

14:00-14:30 Xingzhi Zhan [p.17]

Algebraically positive matrices

14:30-15:00

Jianlong Chen [p.8]

Characterizations and representations of

Moore-Penrose inverses, group inverses and core inverses

15:00-15:30

Junfeng Yin [p.16]

Modulus-based matrix splitting methods for linear complementary

problem



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Speaker&Title Chair

15:45-16:15 Jungong Xue [p.16]

Performance enhancement of doubling algorithms for a class of

complex nonsymmetric algebraic Riccati equations

Fuzhen

Zhang

16:15-16:45

Jianzhou Liu [p.12] The solution bounds and fixed point iterative algorithm for

the discrete coupled algebraic Riccati equation

applied to automatic control

16:45-17:15

Tongsong Jiang [p.9]

Algebraic techniques for Schrodinger equations

in split quaternionic mechanics

17:15-17:45

Qingxiang Xu [p.15]

Norm estimations for the Moore --Penrose inverse of multiplicative

perturbations of matrices

17:45-18:30 Dinner Session 2

Time Siyuan Hall (思源厅)—乐乎新楼 2 号楼一楼


13:30-14:00 Yimin Wei [p.14]

Solving Multi-Linear Systems with M-Tensors

Yang Zhang

14:00-14:30

Xiaodong Zhang [p.17] The Eigenvalues and Signless Laplacian Coefficients of

Graphs

14:30-15:00 Jianzhen Liu [p.12]

Toeplitz matrices are unitarily similar to symmetric matrices

15:00-15:30

Rui-Ping Wen [p.14]） The generalized HSS method with a flexible shift-parameter for

non-Hermitian positive definite linear systems


Time Siyuan Hall (思源厅)—乐乎新楼 2 号楼一楼

Speaker&Title Chair

15:45-16:15 Aihua Li [p.10]

Randic Matrices and Energy of Cycle Based Graphs Yimin Wei

16:15-16:45 Yang Zhang [p.18]

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Computing Generalized Inverses of Ore Matrices

16:45-17:05

Zhaolin Jiang [p.9]

Explicit inversion and generalized inversion of

conjugate-Toeplitz matrices and conjugate-Hankel matrices

17:05-17:25 Kai-Liang Lin [p.11]

The Hurwitz-Radon matrix equation over classical groups

17:25-17:45 Meixiang Chen [p.8]）

Some discussions on the generalized quadratic matrices

17:45-18:30 Dinner

June 10, 2016 (Friday)



08:15-08:45 Ren-Cang Li [p.10]

Ubiquitous Doubling Algorithms, General Theory, and Applications

Jiyuan

Tao

08:45-09:15

Tin-Yau Tam [p.13]

Hyperbolic geometry of positive definite matrices associated with

geometric mean

09:15-09:45 Raymond Nung-Sing Sze [p.13]

Linear preservers of tensor products of rank one matrices

09:45-10:15 Hwa-Long Gau [p.8]

Numerical Radius of Hadamard Product of Matrices




10:30-11:00 Takeaki Yamazaki [p.16]

On interpolational means and an application

Fuzhen

Zhang

11:00-11:30 Ngai-Ching Wong [p.15]

Linear orthogonality preservers of standard operator algebras

11:30-12:00 Jiyuan Tao [p.13]

Some trace inequalities in Euclidean Jordan algebras

12:00-12:30 Minghua Lin [p.12]

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Hua matrix and inequalities involving contractive matrices

12:30-13:15 Lunch

- Good Bye -

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Abstracts

Title: Non-linear inequalities for positive linear maps

Speaker: Man-Duen Choi, University of Toronto, Canada

Abstract: It is impossible to classify all positive linear maps on full matrix algebras.

Nevertheless, there are non-linear inequalities to conquer all quantum entanglements.

Title: Characterizations and representations of Moore-Penrose inverses, group inverses

and core inverses

Speaker: Jianlong Chen, Southeast University

Abstract: Moore-Penrose inverses and group inverses are very important generalized

inverses. Core inverse of a complex matrix was first introduced by Baksalary and Trenkler in

2010. Rakic, Dincic and Djordjevic generalized this notion to the case of a ring in 2014. In

this talk, we will give some new characterizations and representations of Moore-Penrose

inverses, group inverses and core inverses, by using equations and units in a ring.

Title: Some discussions on the generalized quadratic matrices

Speaker: Meixiang Chen, Putian University & Fujian Normal University

Abstract: In 2005, for a given idempotent matrix , Farebrother and Trenkler

introduced a matrix class---generalized quadratic matrix as follows

We find that the uniqueness of expression for generalized quadratic matrices is not only

concerned with the properties of , but also with the rank of . We will divide the set

into the union of four disjointed subsets, and then obtain the sufficient and necessary

conditions for the uniqueness of generalized quadratic matrices’ expression. As applications,

some related discussions about generalized quadratic matrices are made as well.

Title: Numerical Radius of Hadamard Product of Matrices

Speaker: Hwa-Long Gau, National Central University, Taiwan

Abstract: It is known that the numerical radius of the Hadamard product of two

-by- matrices and is related to those of and by

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(a) ,

(b) if one of and is normal, and

(c) if is positive semidefinite. In this talk, we

give complete characterizations of and for which the equality is attained. The

matrices involved can be considered as elaborate generalizations of the equality--attaining

and for (a), ( ) and for

(b), and ( ) and for (c).

Co-author: Peiyuan Wu

Title: Explicit inversion and generalized inversion of conjugate-Toeplitz matrices and

conjugate-Hankel matrices

Speaker: Zhaolin Jiang, Linyi University

Abstract: In this talk, the inverses and generalized inversion of conjugate-Toeplitz (CT) and

conjugate-Hankel (CH) matrices can be expressed by the Gohberg-Heinig type formula. We

obtain an explicit inverse and generalized inversion formula of conjugate-Toeplitz

matrix. Similarly, the formula and the decomposition of the inverse and generalized

inversion of a conjugate-Hankel matrix are provided. Also the stability of the inverse

and generalized inversion formulas of CT and CH matrices are discussed. Examples are

provided to verify the feasibility of the algorithms.

Title: Algebraic techniques for Schrodinger equations in split quaternionic mechanics

Speaker: Tongsong Jiang, Heze University

Abstract: In the study of theory and numerical computations of split quaternionic mechanics

and chemistry, one of important tasks is to solve split quaternionic Schrodinger equation

with A a split quaternion matrix, and a split quaternion eigenstate to A.

The split quaternionic Schrodinger equation plays an important role in split quaternionic

mechanics and chemistry, and the study of the split quaternionic Schrodinger equation is

reduced to the study of split quaternionic eigen-problem with A a split quaternion

matrix. This paper, by means of a real representation of split quaternion matrices, studies

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problems of split quaternionic Least Squares eigen-problem , and give algebraic techniques

of finding eigenvalues and eigenvectors of a split quaternion matrix in split quaternionic

mechanics.

Title: Three qubit separability criteria with diagonal and anti-diagonal entries

Speaker: Seung-Hyeok Kye, Seoul National University, Korea

Abstract: We give separability criteria for three qubit states in terms of diagonal and

anti-diagonal entries. In this criteria, the arguments of anti-diagonal entries play key roles.

They turn out to be necessary and sufficient for -shaped states whose anti-diagonal entries

share common absolute values. In some cases, the arguments must obey an identity relation.

With this relation, we completely characterize separability of -shaped three qubit states

whose ranks are less than or equal to six.

Co-author: Kyung Hoon Kim (The University of Suwon)

Title: Randic Matrices and Energy of Cycle Based Graphs

Speaker: Aihua Li, Montclair State University, USA

Abstract: In this research, we investigate Randic matrices of certain cycle based graphs.

Spectra and energy of the matrices are studied. We give a bound for the eigenvalues.

Behavior and properties of certain eigenvalues are provided.

Co-author: Jhonny Almeida

Title: Linear and non-linear matrix inequalities

Speaker: Chi-Kwong Li, College of William and Mary, USA & Shanghai University

Abstract: We use multilinear and quadratic form techniques to obtain some linear and

non-linear matrix inequalities involving generalized matrix functions.

Co-authors: Shaowu Huang, Yiu-Tung Poon, Qing-Wen Wang.

Title: Ubiquitous Doubling Algorithms, General Theory, and Applications

Speaker: Ren-Cang Li, University of Texas at Arlington, USA

Abstract: Iterative methods are widely and indispensably used in numerical approximations.

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Basically, any iterative method is a rule that produces a sequence of approximations and with

a reasonable expectation that newer approximations in the sequence are better. The goal of a

doubling algorithm is to significantly speed up the approximation process by seeking ways

to skip computing most of the approximations in the sequence but sporadically few, in fact,

extremely very few: only the -th approximations in the sequence, kind of like computing

via repeatedly squaring. However, this idea is only worthwhile if there is a much

cheaper way to directly obtain the -th approximation from the -th one than simply

following the rule to generates every approximations between the -th and -th

approximations in order to obtain the -th approximation. Anderson (1978) had sought the

idea to speed up the simple fixed point iteration for solving the discrete-time algebraic

Riccati equation via repeatedly compositions of the fixed point iterative function. As can be

imagined, under repeatedly compositions, even a simple function can usually and quickly

turn into nonetheless a complicated and unworkable one, which is the case in Anderson’s

doubling iterations. In the last 20 years or so in large part due to an extremely elegant way of

formulation and analysis, the researches in doubling algorithms thrived and continues to be

very active, leading to numerical effective and robust algorithms not only for the

continuous‐time and discrete‐time algebraic Riccati equations from optimal control that

motivated the researches in the first place but also for -matrix algebraic Riccati equations

(MARE), structured eigenvalue problems, and other nonlinear matrix equations. But the

resulting theory is somewhat fragmented and sometimes ad hoc. In this talk, we will seek to

provide a general and coherent theory, discuss new highly accurate doubling algorithm for

MARE, and look at several important applications.

Co-authors: Tsung-Ming Huang (National Taiwan Normal University) and Wen-Wei Lin

(National Chiao Tung University)

Title: Convergence of products of independent random matrices

Speaker: Ming Liao, Auburn University, USA

Abstract: We extend the well-known Kolmogorov's three series theorem for the convergence

of infinite sums of independent random variables to infinite products of independent random

matrices. As application, we present a simple necessary and sufficient condition in the case

of normally distributed random matrices

Title: The Hurwitz-Radon matrix equation over classical groups

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Speaker: Kai-Liang Lin, Northwest A&F University

Abstract: 我们将关于复正交群和实正交群的 Hurwitz-Radon 定理这一经典结果，推广到任意的域上的三

类典型群（线性群、正交群和辛群），这些工作是上世纪 40-50 年代华罗庚和 Jean Dieudonné 的延续。特

别的，本文完善了华罗庚 1947 年论文的结果，得到了经典的 Hurwitz-Radon 定理的一个辛类比。

Title: Hua matrix and inequalities involving contractive matrices

Speaker: Minghua Lin, Shanghai University

Abstract: The Hua matrix is an inspiring source for matrix inequalities. In this talk, I will

further examine the eigenvalue or singular value relations between the diagonal and

off-diagonal blocks of the Hua matrix; these are in the form of inequalities involving

contractive matrices.

Title: Toeplitz matrices are unitarily similar to symmetric matrices

Speaker: Jianzhen Liu, Auburn University, USA

Abstract: We prove that Toeplitz matrices are unitarily similar to complex symmetric

matrices. Moreover, an unitary matrix that uniformly turns all Toeplitz

matrices via similarity to complex symmetric matrices is explicitly given. When , we

prove that each complex symmetric matrix is unitarily similar to some Toeplitz matrix, but

the statement is false when .

Co-authors: Mao-Ting Chien, Hiroshi Nakazato and Tin-Yau Tam

Title: The solution bounds and fixed point iterative algorithm for the discrete coupled

algebraic Riccati equation applied to automatic control

Speaker: Jianzhou Liu, Xiangtang University

Abstract: In this paper, applying the special properties of nonnegative matrices and

symmetric matrices, we consider the coupled term as a whole and derive the solution bounds

of the discrete coupled algebraic Riccati equation. This reduces the error of taking apart the

coupled term separately when applying inequality techniques to get the bounds in general.

Then, using Cauchy-Schwarz inequality, matrix norm inequalities and a fixed point theorem,

we discuss the existence uniqueness condition and fixed point iteration for the solution of

this equation. Finally, we offer corresponding numerical examples to illustrate the

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effectiveness of our results.

Co-authors: Juan Zhang, Li Wang

Title: One horse racing story, two card games, and three matrix theorems

Speaker: Yiu-Tung Poon, Iowa State University, USA

Abstract: We discuss two card games motivated by an ancient horse racing story in China

and the connection with three matrix theorems.

Co-author: Chi-Kwong Li.

Title: Linear preservers of tensor products of rank one matrices

Speaker: Raymond Nung-Sing Sze, The Hong Kong Polytechnic University, Hong Kong

Abstract: In recent years, linear maps that preserve certain properties of tensor products

were studied by many researchers. In this talk, we will briefly review these results and give a

characterization of linear maps that preserve tensor products of rank one matrices, i.e.,

characterizing linear maps such that

for all , and .

Co-authors: Zejun Huang (Hunan University), Shiyu Shi (The Hong Kong Polytechnic

University).

Title: Hyperbolic geometry of positive definite matrices associated with geometric mean

Speaker: Tin-Yau Tam, Auburn University, USA

Abstract: In this talk we will discuss the geometry and inequalities associated with the

geometric mean of positive definite matrices. The space of positive definite

matrices of determinant 1 is a Riemannian manifold. It turns out that the geometry

associated with the Riemannian structure is hyperbolic. We show that geodesic convexity

emerges when a natural pre-order call log majorization is introduced to . Some

inequalities for the geometric mean reflect the hyperbolic geometry.

Co-authors: Trung Hoa Dinh, Ming Liao, Xuhua Liu

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Title: Some trace inequalities in Euclidean Jordan algebras

Speaker: Jiyuan Tao, Loyola University Maryland, USA

Abstract: In matrix theory, the Thompson triangle inequality, Golden-Thompson

inequality, and Araki-Lieb-Thirring inequality are well known. In this talk, we present a

generalization of these three inequalities, respectively, to the setting of Euclidean Jordan

algebras.

Title: Solving Multi-Linear Systems with M-Tensors

Speaker: Yimin Wei, Fudan University

Abstract: This talk is concerned with solving some structured multi-linear systems,

especially focusing on the equations whose coefficient tensors are M-tensors, or called

M-equations for short. We prove that a nonsingular M-equation with a positive right-hand

side always has a unique positive solution. Several iterative algorithms are proposed for

solving multi-linear nonsingular M-equations, generalizing the classical iterative methods

and the Newton method for linear systems. Furthermore, we apply the M-equations to some

nonlinear differential equations and the inverse iteration for spectral radii of nonnegative

tensors.

Co-author: Weiyang Ding

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Title: The generalized HSS method with a flexible shift-parameter for non-Hermitian

positive definite linear systems

Speaker: Rui-Ping Wen, Taiyuan Normal University

Abstract: Based on the Hermitian and skew-Hermitian splitting (HSS) (see [1]), we come

up with a generalized HSS iteration method with a flexible shift-parameter for solving the

non-Hermitian positive definite system of linear equations. This iteration method utilizes the

optimization technique to obtain the optimal value of the flexible shift-parameter at iteration

process. Both theory and experiment have shown that the new strategy is efficient.

[1] Z.-Z. Bai, G.H. Golub, M.K. Ng, Hermitian and skew-Hermitian splitting methods for

non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl. 24(2003)

603-626.

Title: Linear orthogonality preservers of standard operator algebras

Speaker: Ngai-Ching Wong, National Sun Yat-sen University, Taiwan

Abstract: In 2003, Araujo and Jarosz showed that every bijective linear map

between unital standard operator algebras preserving zero products in two ways is a scalar

multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results

hold if both are unital standard algebras on Hilbert spaces and preserves range or

domain orthogonality. In particular, such maps are automatically bounded. In this paper, we

will study linear orthogonality preservers in a unified way. We will show that every

surjective linear map between standard operator algebras preserving range/domain

orthogonality carries a standard form, and is thus automatically bounded.

Co-author: Chung-Wen Tsai.

Title: Companion Matrices: Numerical Range, Crawdord Number and Zero-dilation

Index

Speaker: Pei Yuan Wu, National Chiaotung University, Taiwan

Abstract: The companion matrices play the role of the building blocks for the rational form

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of matrices in general. In this talk, we will discuss several properties of such matrices such

as (1) their (unitary) reducibility, (2) the circularity of their numerical ranges and the line

segments on the boundary of the numerical ranges, (3) the estimates of their Crawwford

numbers (= the distance from the origin to the boundary of the numerical range), and (4) the

zero-dilation indices of such matrices (= the largest size of the zero matrix which can be

dilated to the matrix).

Title: Norm estimations for the Moore --Penrose inverse of multiplicative perturbations

of matrices

Speaker: Qingxiang Xu, Shanghai Normal University

Abstract：A multiplicative perturbation of a matrix is of , where and

are square matrices. This talk will focus on representations of the Moore-Penrose inverse

, and some norm estimations for . Some new ideals and techniques will be

presented.

Title: Performance enhancement of doubling algorithms for a class of complex

nonsymmetric algebraic Riccati equations

Speaker: Jungong Xue, Fudan University

Abstract: A new class of complex nonsymmetric algebraic Riccati equations has been

studied by Liu and Xue (2012, Complex nonsymmetric algebraic Riccati equations arising in

Markov modulated fluid flows, SIAM J. Matrix Anal. Appl., 33, 569-596), which is related to

the -matrix algebraic Riccati equations. Doubling algorithms, with properly chosen

parameters, are used there for equations in this new class. It is pointed out that the number of

iterations for the doubling algorithms may be relatively large in some situations. In this talk,

we show that the performance of the doubling algorithms can often be improved

significantly if a proper preprocessing procedure is used on the give Riccati equation.

Numerical experiments show that this preprocessing procedure is very effective.

Co-author: Chun-Hua Guo and Changli Liu.

Title: On interpolational means and an application

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Speaker: Takeaki Yamazaki, Toyo University, Japan

Abstract: For a weighted operator mean with a weight , J.I. Fujii and Kamei have

considered operator interpolational property as follows.

for all and positive definite operators . We call the family of weighted

operator means satisfying the above property the interpolational mean. In this

talk, we shall introduce a characterization of the interpolationa mean. To give the

characterization, we shall introduce the algorithms to give a weighted operator mean form an

arbitrary operator mean. Next, we shall give an integral representation of operator means via

the interpolational means.

Co-authors: Yoichi Udagawa (Tokyo University of Science) and Masahiro Yanagida (Tokyo

University of Science)

Title: Modulus-based matrx splitting methods for linear complementary problem

Speaker: Jun-Feng Yin, Tongji university

Abstract：For the large sparse linear complementarity problem, a class of accelerated

modulus-based matrix splitting iteration methods is established by reformulating it as a

general implicit fixed-point equation, which covers the known modulus-based matrix

splitting iteration methods. The convergence conditions are presented when the system

matrix is either a positive definite matrix or an H +-matrix. Numerical experiments further

show that the proposed methods are efficient and accelerate the convergence performance of

the modulus-based matrix splitting iteration methods with less iteration steps and CPU time.

Title: Algebraically positive matrices

Speaker: Xingzhi Zhan, East China Normal University, China

Abstract: We introduce the concept of algebraically positive matrices and investigate some

basic properties, including a characterization, the index of algebraic positivity, and sign

patterns that allow or require this property. We also pose two open problems.

Title: Are these permanent conjectures becoming permanent? -- An update on a few

conjectures on permanent

19

Speaker: Fuzhen Zhang, Nova Southeastern University, USA

Abstract: Permanent is one of the most important functions of matrices. The van der

Waerden conjecture (1926-1981) on the permanent of doubly stochastic matrices was once a

long standing and intriguing problem. This talk is concerned with a few conjectures on

permanent that are easily stated but hard to solve. Some are recently settled (by

Shchesnovich and Drury); some are still open.

Title: The Eigenvalus and Signless Laplacian Coefficients of Graphs

Speaker: Xiaodong Zhang, Shanghai Jiao Tong University

Abstract: Let be the characteristic

polynomial of the signless Laplacian matrix of a graph of order . This talk introduces

some properties of the signless Laplacian coefficients of graphs, in particular for tree,

unicyclic and bicyclic graphs. Moreover, we present some relationship between the

incidence energy and the signless Laplacian coefficients of graphs.

Co-authors: Guangjun Zhang and Jie Zhang

Title: Computing Generalized Inverses of Ore Matrices

Speaker: Yang Zhang, University of Manitoba, Canada

Abstract: Ore matrices are matrices over Ore algebras (both differential operators and

difference operators). It has a long research history in algebra, at least dated back to

Jacobson’s seminal work in 1940s, and has been used in many other areas; for example,

control theory and solving differential equations.

In this talk, we will discuss the generalized inverses of Ore matrices. Using one-sided gcd,

lcm and Jacobson’s normal forms, we give algorithms to compute -inverses and

Moore-Penrose inverses of Ore matrices.

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List of Participants

No Name Institute Email

1 Jing Cai 蔡静 Huzhou Teachers College [email protected]

2 Haixia Chang

常海霞 Shanghai Finance University [email protected]

3 Zhen Chao

晁震 East China Normal University [email protected]

4 Guoliang Chen

陈果良 East China Normal University [email protected]

5 Meixiang Chen

陈梅香 Putian University [email protected]

6 Xiaoting Chen

陈晓婷 Linyi University [email protected]

7 Jianlong Chen

陈建龙 Southeast University [email protected]

8 Zhengjie Cheng

程正杰 Hefei University of Technology [email protected]

21

9 Man-Duen Choi University of Toronto, Canada [email protected]

10 Delin Chu National University of Singapore [email protected]

11 Wei-Yang Ding Fudan University [email protected]

12 Tingting Feng

冯亭亭 East China Normal University [email protected]

13 Weiguo Gao Fudan University [email protected]

14 Huishuang Gao

高会双

Inner Mongolia University for

Nationalities [email protected]

15 Hwa-Long Gau National Central University, Taiwan [email protected]

16 Guichun Han

韩贵春

Inner Mongolia University for The


17 Xin Hou 侯欣 Beihang University [email protected]

18 Yunying Huang

黄云英 East China Normal University [email protected]

19 Tongsong Jiang Heze University [email protected]

20 Zhaolin Jiang Linyi University [email protected]

21 Yalei Jin 晋亚

磊 Shanghai Normal University [email protected]

22 Seung-Hyeok

Kye Seoul National University, Korea [email protected]

23 Aihua Li Montclair State University, USA [email protected]

24 Aijun Li 李爱

军 Henan Polytechnic University [email protected]

25 Chi-Kwong Li College of William and Mary, USA

& Shanghai University [email protected]

26 Hanyu Li 李寒

宇 Chongqing University [email protected]

27 Libing Li 李立

斌 Yangzhou University [email protected]

28 Ren-Cang Li University of Texas at Arlington,

USA [email protected]

29 Shangzhi Li

李尚志 Beihang University [email protected]

30 Wenwei Li 李

文伟

University of Science and

Technology of China [email protected]

22

31 Yuan Li 李愿 Shaanxi Normal University [email protected]

32 Guaojun Liao University of Texas at Arlington,

USA

33 Ming Liao Auburn University, USA [email protected]

34 Kailiang Lin

林开亮 Northwest A&F University [email protected]

35 Jianzhen Liu Auburn University, USA [email protected]

36 Jianzhou Liu

刘建州 Xiangtan University [email protected]

37 Shuai Liu 刘帅 Northwest A&F University

38 Xin Liu 刘新 Macau University of Science and

Technology, Macau [email protected]

39 Yonghui Liu

刘永辉

Shanghai University of International

Business and Economics [email protected]

40 Xiangrong Nie

聂祥荣 Bijie University [email protected]

41 Yiu-Tung Poon Iowa State University， USA [email protected]

42 Yaru Qi 齐雅茹 Inner Mongolia University of

Technology [email protected]

43 Jiang Qian 钱

江

Beijing University of Posts and

Telecommunications [email protected]

44 Shuqian Shen

申淑谦 China University Of Petroleum [email protected]

45 Xingping Sheng

盛兴平 Fuyang Normal University [email protected]

46 Jian Shi 时坚 Hebei University [email protected]

47 Guangjing Song

宋广景 Weifang University [email protected]

48 Zhiling Sun

孙志玲

Inner Mongolia University for


49 Raymond

Nung-Sing Sze

The Hong Kong Polytechnic

University, Hong Kong [email protected]

50 Tin-Yau Tam Auburn University, USA [email protected]

51 Jichen Tao

陶继成 China Jiliang University [email protected]

52 Jiyuan Tao Loyola University, USA [email protected]

23

53 Guangbin Wang

王广彬

Qingdao University of Science &


54 Hongxing Wang

王宏兴 Huainan Normal University [email protected]

55 Maoxiang Wang

王茂香 Linyi University [email protected]

56 Qingwen Wang

王卿文 Shanghai University [email protected]

57 Xuezhong Wang Fudan University [email protected]

58 Yimin Wei

魏益民 Fudan University [email protected]

59 Rui-Ping Wen

温瑞萍 Taiyuan Normal University [email protected]

60 Ngai-Ching

Wong

National Sun Yat-sen University,

Taiwan [email protected]

61 Peiyuan Wu National Chiao Tung University,

Taiwan [email protected]

62 Zhongcheng Wu

吴中成

Shanghai University Of Engineering

Science [email protected]

63 Chaoping Xing Nanyang Techonlogy University,

Singapore [email protected]

64 Weiru Xu

徐伟孺 East China Normal University [email protected]

65 Changqing Xu

徐常青

Suzhou University of Science and


66 Jungong Xue Fudan University [email protected]

67 Takeaki

Yamazaki Toyo University, Japan [email protected]

68 Yucheng Yang

杨玉诚 Beihang University [email protected]

69 Zhongpeng

Yang 杨忠鹏 Minnan Normal University [email protected]

70 Jinjiang Yao

姚金江 Linyi University [email protected]

71 Junfeng Yin

殷俊峰 Tongji University [email protected]

72 Guihai Yu

于桂海

Shandong Institute of Business and


73 Shaowen Yu

俞绍文

East China University of Science

and Technology [email protected]

74 Jiangtao Yuan

原江涛 Henan Polytechnic University

24

75 Leihong Zhang Shanghai University of Finance and

Economics [email protected]

76 Xingzhi Zhan

詹兴致 East China Normal University [email protected]

77 Fuzhen Zhang Nova Southeastern, University,

Florida, USA [email protected]

78 Jie Zhang 张杰 Shanghai Finance University [email protected]

79 Xiaodong

Zhang 张晓东 Shanghai Jiao Tong University [email protected]

80 Zhaozhong

Zhang 张兆忠 Linyi University [email protected]

81 Yang Zhang University of Manitoba, Canada [email protected]

82 Jianli Zhao

赵建立 Liaocheng University [email protected]

83 Jianxing Zhao

赵建兴 Guizhou University for Nationalities [email protected]

84 Kun Zhao 赵琨 Linyi University [email protected]

85 Bing Zheng

郑兵 Lanzhou University [email protected]

86 Hongxiu Zhong

仲红秀 East China Normal University [email protected]

87 Duanmei Zhou

周端美 Gannan Normal University [email protected]

88 Zhuoheng He

何卓衡 Shanghai University [email protected]

89 Zhentao He

何振涛 Shanghai University [email protected]

90 Guangda Hu

胡广大 Shanghai University [email protected]

91 Shaowu Huang

黄少武 Shanghai University [email protected]

92 Xiaomei Jia

贾筱楣 Shanghai University [email protected]

93 Yijun Li 李怡

君 Shanghai University [email protected]

94 Jie Li 厉洁 Shanghai University [email protected]

95 Minghua Lin

林明华 Shanghai University [email protected]

96 Juntong Liu Shanghai University [email protected]

25

97 Yangyang Qin

秦洋洋 Shanghai University [email protected]

98 Fangfang Sun

孙方芳 Shanghai University [email protected]

99 Jiancai Sun

孙建才 Shanghai University [email protected]

100 Wanmei Xu

许万美 Shanghai University [email protected]

101 Jinwei Xu

许金炜 Shanghai University [email protected]

102 Xiaoxiao Yang

杨晓晓 Shanghai University [email protected]

103 Jiao Zhang

张姣 Shanghai University [email protected]

104 Fayou Zhao

赵发友 Shanghai Unviersity [email protected]

26

上海大学数学系简介

上海大学是国家“211 工程”重点建设高校之一。上海大学数学系现有教职工

110 人，专职教师 96 人，教授 24 名，博士生导师 23 人，副教授 30 人，国

家千人计划专家 2 名、长江学者 1 名、杰青 1 名、上海千人 1 名、上海领军

人才 1 名、曙光学者 1 名、上海浦江人才计划 4 名，45 岁以下博士比例 100%，

获得海外学位或有海外研究经历的人员比例为 90%；在校本科生 500 多人、硕

士研究生 200 多人、博士研究生 60 多人。

数学系有数学一级学科博士点、数学博士后流动站，数学、系统科学、统计

学三个一级学科硕士点；有上海市教委重点学科——数学科学与技术、上海市重

点学科——运筹与控制、上海高校一流学科、上海市高校高原学科——数学。在

2008 到 2020 年上海市高校发展定位规划中，上海大学数学学科被列为“国家级”

一线学科和“扶强”重点发展学科；上海市应用数学与系统科学研究所、上海大

学核心数学研究所、上海大学优化开放实验室、上海大学数学与编码密码研究所、

上海大学系统科学研究所、上海大学张量与矩阵研究中心均挂靠数学系；上海

市青少年科技人才培养基地—上海大学数学科学实践工作站是全国首家数学工

作站。

2016 年 USNEWS（《美国新闻和世界报导》）全球最佳大学数学学科排名上

海大学位居第 61、英国国际高等教育资讯机（Quacquarelli Symonds, QS）发布

的 “2012 世界大学数学专业排行榜”中，全球排名并列第 51 名；美国 ESI 数

据库最新数据，全球前 1%的数学研究机构有 235 个，上海大学排第 123, 进入

全球前 5‰行列。近年来数学系每年有 200 多位国内外著名专家学者前来讲学

交流，包括菲尔兹奖得主 Zelmanov 及欧拉金质奖章得主陈关荣、杨乐等 30 多

位海内外院士来上海大学数学系访问和科学合作研究。主办或承办了包括“第

14 届国际线性代数协会年会”在内的大型国际学术会议 30 多次。

27

Shanghai University Map (Baoshan Campus)

Lehu Hotel

虹虹桥机场、火车

Hongqiao Airpor

Railway Station

车站

rt、

M

上

S

28

Metro M

上海大学

HU

ap

上海火车站 Shanghai Railw

人民Nanji

way Stat

浦东机场

Pudong Ai

民广场、南京路 ing Road

irport

29

Metro Map

2016 June SHU Matrix Program Plenary - june6 - final 1cklixx.people.wm.edu/mime2016program.pdf ·...

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