Convergence of Nonstationary Iterative Methods for Solving Singular Linear Equations with Index One

被引：2

作者：

Ma, Haifeng ^{[1
]}

Xiao, Cheng ^{[2
]}

机构：

[1] Harbin Normal Univ, Sch Math Sci, Harbin 150025, Heilongjiang, Peoples R China

[2] Shanghai Technolgy Co Ltd, Dept Res, Shanghai, Peoples R China

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Group inverse; index one; multisplitting iterative scheme; P-regular splitting; quotient convergence; singular linear equations; QUOTIENT CONVERGENCE; SYSTEMS; GMRES; MATRICES; INVERSE;

D O I：

10.1080/01630563.2017.1347571

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the nonstationary iterative scheme for solving consistent singular linear system with index one. We utilize the group inverse to present a sufficient condition for the convergence of the nonstationary iterative method. Our result extends the known results of the stationary iterative scheme. Finally, we present a sufficient condition for the multisplitting algorithm and provide numerical examples to illustrate the advantages of nonstationary method.

引用

页码：1507 / 1525

页数：19

共 36 条

[21]

Migallon V, 1996, NUMER LINEAR ALGEBR, V3, P413, DOI 10.1002/(SICI)1099-1506(199609/10)3:5<413::AID-NLA91>3.0.CO

[22]

2-S

[23] Nonstationary multisplittings with general weighting matrices [J].

Migallón, V ;

Penadés, J ;

Szyld, DB .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2001, 22 (04) :1089-1094

[24] SUBPROPER SPLITTING FOR RECTANGULAR MATRICES [J].

NEUMANN, M .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1976, 14 (01) :41-51

[25] REGULAR SPLITTINGS AND DISCRETE NEUMANN PROBLEM [J].

PLEMMONS, RJ .

NUMERISCHE MATHEMATIK, 1976, 25 (02) :153-161

[26] CONVERGENCE OF GENERAL NONSTATIONARY ITERATIVE METHODS FOR SOLVING SINGULAR LINEAR EQUATIONS [J].

Shi, Xinghua ;

Wei, Yimin ;

Zhang, Wen .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2011, 32 (01) :72-89

[27] DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems [J].

Sidi, A .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 335 :189-204

[28] ON THE NUMERICAL ANALYSIS OF OBLIQUE PROJECTORS [J].

Stewart, G. W. .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2011, 32 (01) :309-348

[29] Equivalence of Conditions for Convergence of Iterative Methods for Singular Equations [J].

Szyld, Daniel B. .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 1994, 1 (02) :151-154

[30]

Wang Guorong., 2004, Generalized Inverses: Theory and Computations

← 1 2 3 4 →