隐式重启精化全局Lanczos方法  

IMPLICITLY RESTARTED AND REFINED GLOBAL LANCZOS METHOD

作　　者：刘稳[1] 戴华[1] 

机构地区：[1]南京航空航天大学数学系,南京210016

出　　处：《高等学校计算数学学报》2014年第3期271-288,共18页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11071118)

摘　　要：The numerical methods for solving large symmetric eigenvalue problems are considered in this paper.Based on the global Lanczos process,a global Lanczos method for solving large symmetric eigenvalue problems is presented.In order to accelerate the convergence of the F-Ritz vectors,the refined global Lanczos method is developed.Combining the implicitly restarted strategy with the deflation technique,an implicitly restarted and refined global Lanczos method for computing some eigenvalues of large symmetric matrices is proposed.Numerical results show that the proposed methods are efficient.The numerical methods for solving large symmetric eigenvalue prob- lems are considered in this paper. Based on the global Lanczos process, a global Lanczos method for solving large symmetric eigenvalue problems is presented. In order to accelerate the convergence of the F-Ritz vectors, the refined global Lanczos method is developed. Combining the implicitly restarted strategy with the deflation technique, an implicitly restarted and refined global Lanczos method for computing some eigenvalues of large symmetric matrices is proposed. Numerical results show that the proposed methods are efficient.

关 键 词：LANCZOS方法 矩阵特征值问题 精化 隐式 对称矩阵 工程技术 特征向量 动力分析 

分 类 号：O241.6[理学—计算数学]