题目：Solving Multi-Linear Systems with M-Tensors
时间：2018年12月21日10:00
地点：立志楼A422
主办：数学与计算科学学院
报告人简介：
       魏益民，复旦大学数学科学学院教授，博士生导师。2000.9-2001.6，访问美国哈佛大学和麻省理工学院,任高访学者；2008年荣获“上海高校优秀青年教师”称号；2008年入选上海市‘曙光’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Linear Algebra and its Applications，FILOMAT，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250余篇，与他人合作出版著作《Generalized Inverses: Theory and Computations》(科学出版社，2004年)和英文教材《Numerical Linear Algebra and its Applications》(科学出版社，2004 年)。
报告摘要：
       This paper 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 nonsingularM-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 theM-equations to some nonlinear differential equations and the inverse iteration for spectral radii of nonnegative tensors.