学术报告:2018.6.2-6.3,代数Workshop

发布时间:2018-05-31浏览次数:13

1.
报告人:陈果良教授(华东师范大学)
报告题目:The application of Drazin inverse theory——singular saddle point problems
报告时间:6月2日8:30-9:30
地点:第一报告厅
报告摘要:This talk applies the Drazin inverse theorey to solve singular saddle point problems.  Recently, Bai and Benzi (2017, BIT, Numer. Math. 57 (2017) 287-311) proposed a class of regularized Hermitian and skew-Hermitian splitting (RHSS) iteration methods for solving the nonsingular saddle point problem. In this paper, we apply the Drazin inverse theory and the RHSS method to solve the singular saddle point problem. In the process of the semi-convergence analysis, we get that the RHSS method and the HSS method are unconditionally semi-convergent which has improved the previous results. Some spectral properties of the corresponding preconditioned matrices and a class of improved preconditioned matrices are also analyzed.
报告人简介:陈果良,理学博士,华东师范大学教授。主要研究方向为数值代数,主持完成多项国家自然科学基金面上项目、上海市科委重点项目和上海市教委重点基金。在数学和物理期刊上已发表论文150余篇。

2.
报告人:薛以锋教授(华东师范大学)
报告题目:Stable perturbations of operators: Revisit
报告时间:6月2日9:30-10:30
地点:第一报告厅
报告摘要:In this talk, we will show how the theory of stable perturbations of bounded linear operators on Hilbert spaces or Banach spaces develops. We also give the upper bounds of perturbations of Moore--Penrose inverses, group inverses, Drazin inverses and Metric Moore--Penrose inverse etc. under stable perturbations.
报告人简介:薛以锋,华东师范大学数学系教授、博士生导师,研究方向包括算子代数(K-理论与指标理论‚C*-代数分类)和应用泛函分析(算子广义逆扰动理论;随机矩阵分布理论)。社会兼职:美国数学会会员,上海市数学会会员, 《Mathematical Review》评论员。

3.
报告人:Dragana S. Cvetković Ilić教授(塞尔维亚Niš大学)
报告题目:Various System of Matrix Equations
报告时间:6月2日10:30-11:30
地点:第一报告厅
报告摘要:We will discuss the system of matrix equations AiXBi = Ci, i = 1,2,3,4 and present some necessary and sufficient conditions for its solvability as well as an expression for the general solution. The presented solvability conditions are purely algebraic and the method used in the proof allows a generalization of the obtained results to some more general structures such as algebras of bounded linear operators or rings, under only some additional assumptions concerning regularity. As corollaries we get generalizations of some recent results that involve solving some other systems of matrix equations.
报告人简介:Dragana S. Cvetković Ilić, 塞尔维亚Niš大学教授,主要从事广义逆理论及其应用方面的研究,在Linear Algebra Appl.,Proc. Amer. Math. Soc.,Linear & Multilinear Algebra,J. Austra. Math. Soc.,Acta Math. Sci.,Appl. Math. Comp.,J. Operator Theory等杂志上发表学术论文70余篇,2014年获得塞尔维亚数学会颁发的数学科学成就奖,现兼任Filomat的编委和Facta Universitatis的主编。

4.
报告人:魏益民教授(复旦大学)
报告题目:Solving Multi-linear Systems with M-Tensors
报告时间:6月2日14:00-15:00
地点:第一报告厅
报告摘要: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.
报告人简介:魏益民1997年毕业于复旦大学数学研究所并获得理学博士学位。毕业后留校在数学科学学院工作,2006年4月晋升正教授,计算数学专业博士生导师。2000.9-2001.6访问美国哈佛大学和麻省理工学院,任高级访问学者;现为国际线性代数学会(ILAS) 会员、美国数学会会员、美国工业与应用数学会(SIAM)会员、中国计算数学学会—线性代数专业委员会委员会员,美国数学评论评论员。同时担任FILOMAT、J. Appl. Math. Comput.,以及高校计算数学学报等多个杂志的编委。已在国际国内学术刊物上发表论文300余篇,与他人合作出版著作3本。从事专业为计算数学,主要研究领域包括矩阵广义逆与最小二乘问题、扰动理论与条件数估计、随机算法设计、张量分析与计算等。

5.
报告人:卜长江教授(哈尔滨工程大学)
报告题目:The Inverse and Generalized Inverses of Tensors
报告时间:6月2日15:00-16:00
地点:第一报告厅
报告摘要:In this talk, we give some properties and formulas for the inverse and generalized inverses of tensors. Further, we use the inverse and generalized inverses to establish some solutions of the multilinear systems represented by tensors. (Joint with Lizhu Sun, Xu, Zhang, Baodong Zheng and Yimin Wei)
报告人简介:卜长江,哈尔滨工程大学教授,博士生导师。现任中国线性代数学会理事,中国运筹学会图论组合分会理事,黑龙江省数学会常务理事。Discussiones Mathematicae Graph Theory、Ars Combinatoria、Linear Algebra and its Applications、Linear and Multilinear Algebra、Applied Mathematics and Computation、Journal of Mathematical Analysis and Applications、Electronic Journal of Linear Algebra, Applied Mathematics Letters、Journal of Computational and Applied Mathematics等杂志审稿人。2008年作为会议主席组织了第四届标号图国际会议,2012年作为会议主席组织了第七届矩阵与算子国际会议,2016年作为会议主席组织了2016超图谱理论国际会议。发表SCI检索论文60余篇。

6.
报告人:许庆祥教授(上海师范大学)
报告题目:A review of the Douglas Majorization Theorem
报告时间:6月2日16:00-17:00
地点:第一报告厅
报告摘要:In this talk, we (with M. S. Moslehian) will investigate some significant generalizations and applications of the celebrated Douglas theorem on equivalence of factorization, range inclusion, and majorization of operators established by Ronald George Douglas.
报告人简介:许庆祥,男,上海师范大学数理学院教授、博士生导师。1967年出生于浙江嵊州;1985—1989年,就读于浙江师范大学数学系,获学士学位;1989—1995就读于复旦大学数学所,获理学硕士、博士学位。1995年到上海师范大学数学系工作至今。目前主要研究领域:算子广义逆和Hilbert C*-模。主持过国家自然科学基金等基金项目。

7.
报告人:邓春源教授(华南师范大学)
报告题目:The Solutions to Some Operator Equations with Corresponding Operators Not Necessarily Having Closed Ranges
报告时间:6月3日8:30-9:30
地点:第一报告厅
报告摘要:In this talk, we will first give the necessary and sufficient conditions for the existence of the solution and obtain the general solution to the equation AXB = B = BXA. The results improve the recent results by M. Vosough (Solutions of the system of operator equations BXA = B = AXB via the *-order, Electron. J. Linear Algebr. 32 (2017) 172-183). 
Then we will give some explicit properties of the one sided-inverses and (B, C)-inverses for linear bounded operators. We study the solvability of the operator equations in the general setting of infinite dimensional Hilbert space with corresponding operators no necessarily having closed range. 
报告人简介:邓春源教授,华南师范大学基础数学博士研究生导师。长期从事泛函分析研究工作,研究方向为算子理论与算子代数,在算子矩阵理论、算子的广义逆理论、量子计算题等方面取得了一系列研究成果。主持或参加多项省部级及国家自然科学基金,在国内外重要学术刊物上发表论文80多篇。

8.
报告人:江兆林教授(临沂大学)
报告题目:Gohberg-Semencul type formulas for group and Drazin inverses of a CUPL-Toeplitz matrix
报告时间:6月3日9:30-10:30
地点:第一报告厅
报告摘要:In this talk, the group and Drazin inverses of a CUPL-Toeplitz matrix are considered. The ideas of recurrence and similarity transformation are employed to develop the Gohberg-Semencul type decomposition formulas for group and Drazin inverse of a CUPL-Toeplitz matrix. In addition, the error analysis of the decomposition formulas is given by the 1-norm, -norm and 2-norm, respectively. Finally, three algorithms for the group inverse and their decomposition of a CUPL-Toeplitz matrix are proposed. In fact, a special Markov chain of GI/M/l type is a CUPL-Toeplitz matrix. (Joint with Yao Yu, Xiangchao Meng and Yanpeng Zheng)
报告人简介:江兆林教授,现任理学院院长,山东省中青年学术骨干,山东省教指委成员、美国数学会评论员、中国线性代数学会副秘书长、中国运筹学会线性规划分会理事。主要从事特殊矩阵的理论、算法及其应用、智能决策、图象处理、数值线代数等方面的研究工作。已在Sci China Math(中国科学)、Applied Mathematics and Computation、Linear Algebra and its Applications、Journal of Computational Mathematics、IET Signal Processing等国内外学术期刊发表学术论文100余篇, 出版专著《循环矩阵》一部,主编、主审高校教材10多部, 主编、主审数学教育类读物8部。先后主持或参与了国家级、省级、省教委等课题17项。先后出访过10个国家(地区)的60多所大学。