I) Title: Look–Back GMRES(m) for Solving Large Nonsysmmetric Linear Systems
Abstract: Development of efficient solvers for solving linear systems Ax = b is one of the most significant issue on the field of computational science and engineering. The GMRES method of Saad and Schultz is a well-known solver as the typical Krylov subspace method for nonsymmetric linear systems. While the GMRES methods show good convergence, it has difficulties in storage and computational costs. To remedy these difficulties, the restart technique is generally used as a practical choice. The restarted version of the GMRES method is called the GMRES(m) method. In this talk, we will focus on a relationship between the GMRES(m) method and the error equation and propose a new variant of the GMRES(m) method. Several numerical results will show that this new variant will be attractive.

 

II) Title: An Interior Eigenvalue Problem and Its Numerical Solution
Abstract: In this talk, we consider a generalized eigenvalue problem, whose eigenvalues are all real. The motivation has come from computational materials science, where specific interior eigenvalues need to be computed. The target eigenvalues are the k-th smallest eigenvalue and a small number of eigenvalues around it. To solve this problem, we propose a numerical approach, which does not compute any other unnecessary eigenvalue.

 

报告人简介: 张绍良, 吉林大学数学系本科 (1983年), 日本筑波大学硕士 (1987年), 博士 (1990年)。日本名古屋大学应用物理系教授 (2005年~至今), 日本中国交流中心主任 (兼职，2014年~至今), East Asia SIAM 秘书长 (2011-2012年度)。主要从事矩阵代数方面的数值方法研究。