Preconditioned GMRES methods with incomplete Givens orthogonalization method for large sparse least-squares problems

被引：7

作者：

Yin, Jun-Feng ^{[1
,2
]}

Hayami, Ken ^{[1
]}

机构：

[1] Natl Inst Informat, Chiyoda Ku, Tokyo 1018430, Japan

[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 226卷 / 01期

关键词：

Least-squares problems; Incomplete Givens orthogonalization methods; GMRES; Preconditioner; CONJUGATE-GRADIENT METHODS; LINEAR-SYSTEMS; FACTORIZATION METHODS; ALGORITHM; EQUATIONS;

D O I：

10.1016/j.cam.2008.05.052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose to precondition the GMRES method by using the incomplete Givens orthogonalization (IGO) method for the solution of large sparse linear least-squares problems. Theoretical analysis shows that the preconditioner satisfies the sufficient condition that can guarantee that the preconditioned GMRES method will never break down and always give the least-squares solution of the original problem. Numerical experiments further confirm that the new preconditioner is efficient. We also find that the IGO preconditioned BA-GMRES method is superior to the corresponding CGLS method for ill-conditioned and singular least-squares problems. Crown Copyright (c) 2008 Published by Elsevier B.V. All rights reserved.

引用

页码：177 / 186

页数：10