An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems

被引：89

作者：

Golub, GH ^{[1
]}

Ye, Q

机构：

[1] Stanford Univ, Sci Comp & Computat Math Program, Dept Comp Sci, Stanford, CA 94305 USA

[2] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2002年 / 24卷 / 01期

关键词：

Krylov subspace; preconditioning; eigenvalue problems;

D O I：

10.1137/S1064827500382579

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present an inverse free Krylov subspace method for finding some extreme eigenvalues of the symmetric definite generalized eigenvalue problem Ax = lambdaBx. The basic method takes a form of inner-outer iterations and involves no inversion of B or any shift-and-invert matrix A - lambda(0)B. A convergence analysis is presented that leads to a preconditioning scheme for accelerating convergence through some equivalent transformations of the eigenvalue problem. Numerical examples are given to illustrate the convergence properties and to demonstrate the competitiveness of the method.

引用

页码：312 / 334

页数：23