Some properties of range restricted GMRES methods

被引：7

作者：

Bellalij, M. ^{[1
]}

Reichel, L. ^{[2
]}

Sadok, H. ^{[3
]}

机构：

[1] Univ Valenciennes, Lab Math & Leurs Applicat, F-59313 Valenciennes, France

[2] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[3] Univ Littoral, Ctr Univ Mi Voix, Lab Math Pures & Appl, F-62228 Calais, France

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 290卷

基金：

美国国家科学基金会;

关键词：

III-posed problem; Iterative method; Truncated iteration; GMRES; RRGMRES; Shifted GMRES; ILL-POSED PROBLEMS; PARAMETER CHOICE RULES; LEAST-SQUARES PROBLEMS; NUMERICAL SOLUTION; SINGULAR SYSTEMS; REGULARIZATION; CONVERGENCE;

D O I：

10.1016/j.cam.2015.05.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The GMRES method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix. GMRES-type methods also have been applied to the solution of linear discrete ill-posed problems. Computational experience indicates that for the latter problems variants of the standard GMRES method, that require the solution to live in the range of a positive power of the matrix of the linear system of equations to be solved, generally yield more accurate approximations of the desired solution than standard GMRES. This paper investigates properties of these variants of GMRES. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：310 / 318

页数：9

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