On the convergence of splittings for semidefinite linear systems
type: Item
instance of: scholarly article
title: On the convergence of splittings for semidefinite linear systems
zbMATH Open document ID: 1152.65045
author: Lijing Lin
author: Yimin Wei
author: Ching-Wah Woo
author: Jieyong Zhou
published in: Linear Algebra and its Applications
publication date: 2008-11-06T00:00:00Z
review text: The authors refer to the classical notion of P-regularity, introduced by \textit{H. B. Keller} [J. Soc. Ind. Appl. Math., Ser. B Numer. Anal. 2, 281--290 (1965; Zbl 0135.37503)] for the solution of singular and semidefinite linear systems by iteration. In this respect they consider stipulations on a splitting \(A=M-N\), which lead to fixed point systems such that the iterative scheme converges to a weighted Moore-Penrose solution of the system. Their result requires less restrictions on the splittings that Keller's P-regularity condition to ensure convergence of the iteration.
reviewed by: Constantin Popa
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5362060
zbMATH Keywords: linear system
zbMATH Keywords: rectangular system
zbMATH Keywords: iterative method
zbMATH Keywords: regularity
zbMATH Keywords: Hermitian positive semidefinite matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2007.12.019
OpenAlex ID: W2085702803
cites work: Generalized inverses. Theory and applications.
cites work: Consistency and Splittings
cites work: Cones and Iterative Methods for Best Least Squares Solutions of Linear Systems
cites work: A note on properties of splittings of singular symmetric positive semidefinite matrices
cites work: On the Convergence of General Stationary Linear Iterative Methods for Singular Linear Systems
cites work: On the solution of singular linear systems of algebraic equations by semiiterative methods
cites work: Preconditionings and splittings for rectangular systems
cites work: On the Solution of Singular and Semidefinite Linear Systems by Iteration
cites work: Computational methods for generalized inverse matrices arising from proper splittings
cites work: On the Convergence of Iterative Methods for Semidefinite Linear Systems
cites work: Schwarz Iterations for Symmetric Positive Semidefinite Problems
cites work: Subproper splitting for rectangular matrices
cites work: Monotonicity and Iterative Approximations Involving Rectangular Matrices
cites work: Q5342712
cites work: A Cramer rule for minimum-norm (T) least-squares (S) solution of inconsistent linear equations
cites work: Subproper and regular splittings for restricted rectangular linear system
cites work: (T,S) splitting methods for computing the generalized inverse and rectangular systems∗
cites work: On the perturbation and subproper splittings for the generalized inverse \(A_{T,S}^{(2)}\) of rectangular matrix \(A\)
cites work: Condition number related with generalized inverse \(A_{T,S}^{(2)}\) and constrained linear systems
DOI: 10.1016/J.LAA.2007.12.019
description: scientific article; zbMATH DE number 5362060