Perturbation analysis of singular linear systems with arbitrary index.
type: Item
instance of: scholarly article
title: Perturbation analysis of singular linear systems with arbitrary index.
zbMATH Open document ID: 1033.65026
DOI: 10.1016/S0096-3003(02)00488-5
author: Jieyong Zhou
author: Yiming Wei
published in: Applied Mathematics and Computation
publication date: 2003-11-25T00:00:00Z
review text: The authors consider linear systems of equations \(Ax=b\), where \(A \in\mathbb{C}^{n \times n}\) is a singular matrix with arbitrary index. The following convergence result for semi-iterative methods [see \textit{J. J. Climent}, \textit{M. Neumann} and \textit{A. Sidi}, J. Comput. Appl. Math. 87, 21--38 (1997; Zbl 0899.65020)] is presented. If \(A\) is singular and \(\text{Ind}(A) = \alpha\), then the semi-iterative sequence \(\{x_m\}\) converges to \(A^Db + (I -AA^D)x_0\) for an arbitrary initial guess \(x_0\). \(A^D\) denotes the Drazin inverse of the matrix \(A\). Furthermore, a perturbation analysis for the system of equations \(A^\alpha A x = A^\alpha b\) is given. Hereby, consistent as well as inconsistent perturbed systems are considered.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 2008969
zbMATH Keywords: singular linear systems
zbMATH Keywords: generalized linear least squares problem
zbMATH Keywords: Drazin inverse
zbMATH Keywords: index
zbMATH Keywords: convergence
zbMATH Keywords: Jordan canonical form
reviewed by: Michael Jung
describes a project that uses: DGMRES
MaRDI profile type: Publication
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full work available at URL: s0096-3003(02)00488-5
OpenAlex ID: W2089235260
description: scientific article; zbMATH DE number 2008969