CONVERGENCE OF GENERAL NONSTATIONARY ITERATIVE METHODS FOR SOLVING SINGULAR LINEAR EQUATIONS

被引：18

作者：

Shi, Xinghua ^{[1
]}

Wei, Yimin ^{[1
,2
]}

Zhang, Wen ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Inst Math, Shanghai 200433, Peoples R China

[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2011年 / 32卷 / 01期

基金：

中国国家自然科学基金;

关键词：

singular linear equations; Moore-Penrose inverse; singular Hermitian positive semidefinite; P-regular splitting; two-stage iterative method; quotient convergence; SYSTEMS; SPLITTINGS;

D O I：

10.1137/10079015X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we analyze the convergence of the general nonstationary iterative methods for solving consistent singular linear equations (in particular, singular Hermitian positive semidefinite linear systems), and we discuss relations of general stationary results and ours. We utilize the quotient convergence to prove the convergence of the two-stage iterative algorithms for solving the consistent singular Hermitian positive semidefinite linear equations.

引用

页码：72 / 89

页数：18

共 50 条

[41] On derivative free cubic convergence iterative methods for solving nonlinear equations
Dehghan, M.
Hajarian, M.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2011, 51 (04) : 513 - 519
[42] The iterative methods with higher order convergence for solving a system of nonlinear equations
Chen, Zhongyuan
Qiu, Xiaofang
Lin, Songbin
Chen, Baoguo
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (07): : 3834 - 3842
[43] CONVERGENCE RESULTS FOR GENERAL LINEAR METHODS ON SINGULAR PERTURBATION PROBLEMS
SCHNEIDER, S
BIT, 1993, 33 (04): : 670 - 686
[44] A general iterative approach for solving the general constrained linear matrix equations system
Karimi, Saeed
Dehghan, Maryam
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2016, 38 (07) : 805 - 818
[45] Control Design for Iterative Methods in Solving Linear Algebraic Equations
Meng, Deyuan
Wu, Yuxin
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2022, 67 (10) : 5039 - 5054
[46] Asynchronous relaxed iterative methods for solving linear systems of equations
Tongxiang G.
Applied Mathematics and Mechanics, 1997, 18 (8) : 801 - 806
[47] Iterative methods for solving linear operator equations in Banach spaces
Chistyakov, P. A.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2011, 17 (03): : 303 - 318
[48] CLASS OF NORMS OF ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR EQUATIONS
KINCAID, DR
NUMERISCHE MATHEMATIK, 1973, 20 (05) : 392 - 408
[49] Asynchronous relaxed iterative methods for solving linear systems of equations
Gu, TX
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 1997, 18 (08) : 801 - 806
[50] CLASS OF NORMS OF ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR EQUATIONS
KINCAID, DR
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (01): : A235 - &

← 1 2 3 4 5 →