Inversion error, condition number, and approximate inverses of uncertain matrices
type: Item
instance of: scholarly article
title: Inversion error, condition number, and approximate inverses of uncertain matrices
zbMATH Open document ID: 0997.65049
DOI: 10.1016/S0024-3795(01)00273-7
author: V. Pereyra
published in: Linear Algebra and its Applications
publication date: 2002-05-15T00:00:00Z
review text: The author proposes an approach to rigorously measure, and reduce the effect, of possibly large, structured perturbation in the computation of an inverse matrix. He defines the structured maximal inversion error, that takes into account the structure and not-necessarily small perturbation size. For infinitesimal perturbation he gets a structure condition number. For a wide class of perturbation structures, he shows how to use the convex semidefinte programming to compute bounds on the structured maximal inversion error and structure condition number, and also to compute an approximate inverse. He points out that when the perturbation in unstructured and additive the classical condition number is recovered and the approximate inverse is an operator related to the total least squares.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 90C22
zbMATH DE Number: 1741660
zbMATH Keywords: structured matrix
zbMATH Keywords: condition number
zbMATH Keywords: inversion error
zbMATH Keywords: approximate inverses
zbMATH Keywords: uncertain matrices
zbMATH Keywords: convex semidefinite programming
zbMATH Keywords: total least squares
reviewed by: R. P. Tewarson
describes a project that uses: mctoolbox
describes a project that uses: Sp
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1741660