Condition number for the \(W\)-weighted Drazin inverse and its applications in the solution of rectangular linear system
type: Item
instance of: scholarly article
title: Condition number for the \(W\)-weighted Drazin inverse and its applications in the solution of rectangular linear system
zbMATH Open document ID: 1089.15008
DOI: 10.1007/BF02831923
author: Xiaoke Cui
author: Huai-An Diao
published in: Journal of Applied Mathematics and Computing
publication date: 2006-02-20T00:00:00Z
review text: The perturbation theory for linear systems \(WAWx=b\), \(A \in {\mathbb R}^{m \times n}\), \(W \in {\mathbb R}^{n \times m} \) is studied. The condition number for the W-weighted Drazin inverse solution of the above system is obtained. In addition, the level-2 condition numbers for the W-weighted Drazin inverse and W-weighted Drazin inverse solution are analyzed.
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5007496
zbMATH Keywords: W-weighted Drazin inverse
zbMATH Keywords: W-weighted Drazin-inverse solution
zbMATH Keywords: linear system
zbMATH Keywords: condition number
zbMATH Keywords: componentwise perturbation
describes a project that uses: DGMRES
reviewed by: Néstor Thome
MaRDI profile type: Publication
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: A Drazin inverse for rectangular matrices
cites work: On condition numbers and the distance to the nearest ill-posed problem
cites work: Structured perturbations of Drazin inverse
cites work: Displacement rank of the Drazin inverse
cites work: Structured perturbations of group inverse and singular linear system with index one
cites work: On the solution of singular linear systems of algebraic equations by semiiterative methods
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: A weighted Drazin inverse and applications
cites work: The representation and approximation of the \(W\)-weighted Drazin inverse of linear operators in Hilbert space.
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: Condition number related with \(W\)-weighted Drazin inverse and singular linear systems
cites work: Generalized inverses: theory and computations
cites work: A characterization for the \(W\)-weighted Drazin inverse and a Cramer rule for the \(W\)-weighted Drazin inverse solution
cites work: Integral representation of the \(W\)-weighted Drazin inverse
cites work: Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers
cites work: On group inverse of singular Toeplitz matrices
cites work: On Drazin inverse of singular Toeplitz matrix
cites work: Q5436051
cites work: A note on the perturbation of the \(W\)-weighted Drazin inverse.
description: scientific article; zbMATH DE number 5007496