INNER-ITERATION KRYLOV SUBSPACE METHODS FOR LEAST SQUARES PROBLEMS

被引：19

作者：

Morikuni, Keiichi ^{[1
]}

Hayami, Ken ^{[2
]}

机构：

[1] Grad Univ Adv Studies Sokendai, Sch Multidisciplinary Sci, Dept Informat, Chiyoda Ku, Tokyo 1018430, Japan

[2] Grad Univ Adv Studies Sokendai, Natl Inst Informat, Dept Informat, Sch Multidisciplinary Sci,Chiyoda Ku, Tokyo 1018430, Japan

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2013年 / 34卷 / 01期

关键词：

least squares problems; iterative method; preconditioner; inner-outer iteration; Krylov subspace method; GMRES method; CG method; Cimmino's method; Kaczmarz's method; SOR method; GMRES METHODS; PRECONDITIONER; SOR;

D O I：

10.1137/110828472

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Stationary inner iterations in combination with Krylov subspace methods are proposed for overdetermined least squares problems. The inner iterations are efficient in terms of computational work and memory and also serve as powerful preconditioners for ill-conditioned and rank-deficient problems. Theoretical justifications for using the inner iterations as preconditioners are presented. Numerical experiments on overdetermined sparse least squares problems show that the proposed methods outperform previous methods, especially for ill-conditioned and rank-deficient problems.

引用

页码：1 / 22

页数：22

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