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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
1
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
2
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
3
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.
2. By Taxi: Directly take taxi to 716 Jingqiu Road, Shanghai University (Baoshan Campus,
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).
2. By Taxi: Directly take taxi to 716 Jingqiu Road, 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).
3. By Taxi: Directly take taxi to 716 Jingqiu Road, 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, m_lin@i.shu.edu.cn
Dr. Jiancai Sun, jcsun@shu.edu.cn
Prof. Qing-Wen Wang, wqw@shu.edu.cn
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)
Time Xuehai Hall (学海厅)—乐乎新楼 2 号楼二楼
Speaker & Title Chair
5
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
Time Xuehai Hall (学海厅)—乐乎新楼 2 号楼二楼
Speaker & Title Chair
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
15:30-15:45 Coffee/Tea Break
Time Xuehai Hall (学海厅)—乐乎新楼 2 号楼二楼
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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
Speaker & Title Chair
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
15:30-15:45 Coffee/Tea Break
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)
Time Xuehai Hall (学海厅)—乐乎新楼 2 号楼二楼
Speaker & Title Chair
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
10:15-10:30 Coffee/Tea Break
Time Xuehai Hall (学海厅)—乐乎新楼 2 号楼二楼
Speaker & Title Chair
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
11
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
15
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
17
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 caijing@hutc.zj.cn
2 Haixia Chang
常海霞 Shanghai Finance University hcychang@163.com
3 Zhen Chao
晁震 East China Normal University zhenchao1120@163.com
4 Guoliang Chen
陈果良 East China Normal University glchen@math.ecnu.edu.cn
5 Meixiang Chen
陈梅香 Putian University 13799004406@126.com
6 Xiaoting Chen
陈晓婷 Linyi University 851190061@qq.com
7 Jianlong Chen
陈建龙 Southeast University jlchen@seu.edu.cn
8 Zhengjie Cheng
程正杰 Hefei University of Technology 490538106@qq.com
21
9 Man-Duen Choi University of Toronto, Canada choi@math.utoronto.ca
10 Delin Chu National University of Singapore matchudl@nus.edu.sg
11 Wei-Yang Ding Fudan University 11110180009@fudan.edu.cn
12 Tingting Feng
冯亭亭 East China Normal University 361835442@qq.com
13 Weiguo Gao Fudan University wggao@fudan.edu.cn
14 Huishuang Gao
高会双
Inner Mongolia University for
Nationalities gaohuishuang@163.com
15 Hwa-Long Gau National Central University, Taiwan hlgau@math.ncu.edu.tw
16 Guichun Han
韩贵春
Inner Mongolia University for The
Nationalities hanguicun@163.com
17 Xin Hou 侯欣 Beihang University houge19870512@126.com
18 Yunying Huang
黄云英 East China Normal University yingzi8869@163.com
19 Tongsong Jiang Heze University jiangtongsong@sina.com
20 Zhaolin Jiang Linyi University jzh1208@sina.com
21 Yalei Jin 晋亚
磊 Shanghai Normal University zzuedujinyalei@163.com
22 Seung-Hyeok
Kye Seoul National University, Korea kye@snu.ac.kr
23 Aihua Li Montclair State University, USA lia@mail.montclair.edu
24 Aijun Li 李爱
军 Henan Polytechnic University liaijun72@163.com
25 Chi-Kwong Li College of William and Mary, USA
& Shanghai University ckli@math.wm.edu
26 Hanyu Li 李寒
宇 Chongqing University hyli@cqu.edu.cn
27 Libing Li 李立
斌 Yangzhou University lbli@yzu.edu.cn
28 Ren-Cang Li University of Texas at Arlington,
USA rcli@uta.edu
29 Shangzhi Li
李尚志 Beihang University lisz@buaa.edu.cn
30 Wenwei Li 李
文伟
University of Science and
Technology of China liwenwei@ustc.edu
22
31 Yuan Li 李愿 Shaanxi Normal University liyuan0401@aliyun.com
32 Guaojun Liao University of Texas at Arlington,
USA
33 Ming Liao Auburn University, USA liaomin@auburn.edu
34 Kailiang Lin
林开亮 Northwest A&F University kailiang_lin@163.com
35 Jianzhen Liu Auburn University, USA jzl0073@auburn.edu
36 Jianzhou Liu
刘建州 Xiangtan University liujz@xtu.edu.cn
37 Shuai Liu 刘帅 Northwest A&F University
38 Xin Liu 刘新 Macau University of Science and
Technology, Macau xiliu@must.edu.mo
39 Yonghui Liu
刘永辉
Shanghai University of International
Business and Economics liuyh@lsec.cc.ac.cn
40 Xiangrong Nie
聂祥荣 Bijie University niexiangrong2004@sina.com
41 Yiu-Tung Poon Iowa State University, USA ytpoon@iastate.edu
42 Yaru Qi 齐雅茹 Inner Mongolia University of
Technology qiyaru2002@163.com
43 Jiang Qian 钱
江
Beijing University of Posts and
Telecommunications jqian104@126.com
44 Shuqian Shen
申淑谦 China University Of Petroleum shuqianshen@126.com
45 Xingping Sheng
盛兴平 Fuyang Normal University xingpingsheng@163.com
46 Jian Shi 时坚 Hebei University mathematic@126.com
47 Guangjing Song
宋广景 Weifang University songguangjiang2005@163.com
48 Zhiling Sun
孙志玲
Inner Mongolia University for
Nationalities yusinmg@126.com
49 Raymond
Nung-Sing Sze
The Hong Kong Polytechnic
University, Hong Kong raymond.sze@polyu.edu.hk
50 Tin-Yau Tam Auburn University, USA tamtiny@auburn.edu
51 Jichen Tao
陶继成 China Jiliang University taojc@cjlu.edu.cn
52 Jiyuan Tao Loyola University, USA mct0006@gmail.com
23
53 Guangbin Wang
王广彬
Qingdao University of Science &
Technology wguangbin750828@sina.com
54 Hongxing Wang
王宏兴 Huainan Normal University winghongxing@163.com
55 Maoxiang Wang
王茂香 Linyi University tiexianer@163.com
56 Qingwen Wang
王卿文 Shanghai University wqw@shu.edu.cn
57 Xuezhong Wang Fudan University xuezhongwang77@126.com
58 Yimin Wei
魏益民 Fudan University ymwei@fudan.edu.cn
59 Rui-Ping Wen
温瑞萍 Taiyuan Normal University wenrp@163.com
60 Ngai-Ching
Wong
National Sun Yat-sen University,
Taiwan wong@math.nsysu.edu.tw
61 Peiyuan Wu National Chiao Tung University,
Taiwan pywu@math.nctu.edu.tw
62 Zhongcheng Wu
吴中成
Shanghai University Of Engineering
Science wzcsues@163.com
63 Chaoping Xing Nanyang Techonlogy University,
Singapore xingcp@ntu.edu.sg
64 Weiru Xu
徐伟孺 East China Normal University weiruxu@foxmail.com
65 Changqing Xu
徐常青
Suzhou University of Science and
Technology cqxurichard@163.com
66 Jungong Xue Fudan University xuej@fudan.edu.cn
67 Takeaki
Yamazaki Toyo University, Japan t-yamazaki@toyo.jp
68 Yucheng Yang
杨玉诚 Beihang University yycalgebra@126.com
69 Zhongpeng
Yang 杨忠鹏 Minnan Normal University yangzhongpeng@126.com
70 Jinjiang Yao
姚金江 Linyi University yaojinjiang@lyu.edu.cn
71 Junfeng Yin
殷俊峰 Tongji University yinjf@tongji.edu.cn
72 Guihai Yu
于桂海
Shandong Institute of Business and
Technology yuguihai@126.com
73 Shaowen Yu
俞绍文
East China University of Science
and Technology yushaowen@ecust.edu.cn
74 Jiangtao Yuan
原江涛 Henan Polytechnic University
24
75 Leihong Zhang Shanghai University of Finance and
Economics longzlh@gmail.com
76 Xingzhi Zhan
詹兴致 East China Normal University zhan@math.ecnu.edu.cn
77 Fuzhen Zhang Nova Southeastern, University,
Florida, USA zhang@nova.edu
78 Jie Zhang 张杰 Shanghai Finance University zhangjie.sjtu@163.com
79 Xiaodong
Zhang 张晓东 Shanghai Jiao Tong University xiaodong@sjtu.edu.cn
80 Zhaozhong
Zhang 张兆忠 Linyi University touchang@163.com
81 Yang Zhang University of Manitoba, Canada yang.zhang@umanitoba.ca
82 Jianli Zhao
赵建立 Liaocheng University zhaojl1964@126.com
83 Jianxing Zhao
赵建兴 Guizhou University for Nationalities zjx810204@163.com
84 Kun Zhao 赵琨 Linyi University zhao_kun1992@sina.cn
85 Bing Zheng
郑兵 Lanzhou University bzheng@lzu.edu.cn
86 Hongxiu Zhong
仲红秀 East China Normal University zhonghongxiu@gmail.com
87 Duanmei Zhou
周端美 Gannan Normal University gzzdm2008@163.com
88 Zhuoheng He
何卓衡 Shanghai University Hzh19871126@126.com
89 Zhentao He
何振涛 Shanghai University bswshzx@163.com
90 Guangda Hu
胡广大 Shanghai University ghu@hit.edu.cn
91 Shaowu Huang
黄少武 Shanghai University Shaowu2050@126.com
92 Xiaomei Jia
贾筱楣 Shanghai University xmjia@shu.edu.cn
93 Yijun Li 李怡
君 Shanghai University 743707522@qq.com
94 Jie Li 厉洁 Shanghai University lijie782929264@qq.com
95 Minghua Lin
林明华 Shanghai University mlin87@ymail.com
96 Juntong Liu Shanghai University juntongliu82@163.com
25
97 Yangyang Qin
秦洋洋 Shanghai University yyqin1991@126.com
98 Fangfang Sun
孙方芳 Shanghai University 458338502@qq.com
99 Jiancai Sun
孙建才 Shanghai University jcsun@shu.edu.cn
100 Wanmei Xu
许万美 Shanghai University wanmeixu@shu.edu.cn
101 Jinwei Xu
许金炜 Shanghai University jwxu1991@126.com
102 Xiaoxiao Yang
杨晓晓 Shanghai University yangxiaoxiao1991@shu.edu.cn
103 Jiao Zhang
张姣 Shanghai University zhangjiao@shu.edu.cn
104 Fayou Zhao
赵发友 Shanghai Unviersity fyzhao@i.shu.edu.cn
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
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