Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers
type: Item
instance of: scholarly article
title: Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers
zbMATH Open document ID: 1077.15007
published in: Journal of Computational and Applied Mathematics
publication date: 2005-06-30T00:00:00Z
review text: The condition number for the Drazin inverse and the Drazin-inverse solution of singular linear systems \(Ax=b\) are investigated under the \(P\)-norm and a componentwise perturbation. The assumptions \(\text{Im}(E) \subseteq \text{Im}(A^k)\) and \(\text{Im}(E^T) \subseteq \text{Im}(A^k)^T\) on the perturbation \(E\) are assumed, where \(\text{Im}(E)\) denotes the range of \(E\), \(E^T\) is the transpose of \(E\) and \(k\) is the index of \(A\).
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 2184019
zbMATH Keywords: Drazin inverse
zbMATH Keywords: Drazin-inverse solution
zbMATH Keywords: singular system
zbMATH Keywords: condition number
zbMATH Keywords: componentwise perturbation
author: Yimin Wei
author: Huai-An Diao
reviewed by: Néstor Thome
describes a project that uses: DGMRES
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: j.cam.2004.11.040
OpenAlex ID: W2035974022
cites work: Generalized inverses. Theory and applications.
cites work: Q3207128
cites work: A semi-iterative method for real spectrum singular linear systems with an arbitrary index
cites work: On condition numbers and the distance to the nearest ill-posed problem
cites work: Structured perturbations of group inverse and singular linear system with index one
cites work: Displacement rank of the Drazin inverse
cites work: Additive results for the generalized Drazin inverse
cites work: On the solution of singular linear systems of algebraic equations by semiiterative methods
cites work: Q5689624
cites work: On the condition number of linear least squares problems in a weighted Frobenius norm
cites work: Condition numbers and their condition numbers
cites work: The perturbation theory for the Drazin inverse and its applications. II
cites work: A Theory of Condition
cites work: New condition numbers for matrices and linear systems
cites work: DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems
cites work: Index splitting for the Drazin inverse and the singular linear system
cites work: Perturbation analysis of singular linear systems with index one∗
cites work: The perturbation theory for the Drazin inverse and its applications
cites work: Condition number of Drazin inverse and their condition numbers of singular linear systems.
cites work: Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index
cites work: The representation and approximation for Drazin inverse
cites work: Additional results on index splittings for Drazin inverse solutions of singular linear systems
cites work: Stagnation analysis of DGMRES.
DOI: 10.1016/J.CAM.2004.11.040
description: scientific article; zbMATH DE number 2184019