A note on the perturbation bound of the Drazin inverse
type: Item
instance of: scholarly article
title: A note on the perturbation bound of the Drazin inverse
zbMATH Open document ID: 1032.15006
DOI: 10.1016/S0096-3003(02)00230-8
author: Xiezhang Li
author: Yimin Wei
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: \textit{N. Gonzalez}, \textit{J. Koliha} and \textit{Y. Wei} [Linear Algebra Appl. 312, 181-189 (2000; Zbl 0963.15002)] or \textit{Y. Wei} [Appl. Math. Comput. 125, 231-244 (2002; Zbl 1025.15004)] have derived bounds for \(\|(A+E)^\#-A^D\|\) where \((\cdot)^\#\) denotes the group inverse and \((\cdot)^D\) denotes the Drazin inverse. These bounds hold when among other conditions, the index of \(A+E\) is 1. In this paper, the latter condition is removed and sharper bounds are obtained (unlike in the previous references, the bound is small when \(\|E\|\) is small). As a special case, a bound is given when \((\cdot)^\#\) is replaced by \((\cdot)^D\).
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 1978085
zbMATH Keywords: Drazin inverse
zbMATH Keywords: group inverse
zbMATH Keywords: perturbation theory
zbMATH Keywords: norm bounds
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
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full work available at URL: s0096-3003(02)00230-8
OpenAlex ID: W1971857991
description: scientific article; zbMATH DE number 1978085