On the sensitivity of the LU factorization
type: Item
instance of: scholarly article
title: On the sensitivity of the LU factorization
zbMATH Open document ID: 0924.65038
DOI: 10.1007/BF02510255
author: Xiao-Wen Chang
author: Christopher C. Paige
published in: BIT
publication date: 1999-03-07T00:00:00Z
review text: The paper presents how \(L\) and \(U\) change as \(A\) changes in the factorization \(A= LU\). The first-order perturbation results are derived in two ways. The so-called matrix-vector equation approach is used to provide sharp bounds, resulting in the condition numbers for the \(L\) and \(U\) factors, while the so-called matrix equation approach is used to obtain more practical bounds, resulting in easily computable upper bounds on the condition numbers. The effect of partial pivoting and complete pivoting on the sensitivity of the \(LU\)-factorization is presented and numerical results are given to illustrate the theoretical analysis.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 1228550
zbMATH Keywords: numerical examples
zbMATH Keywords: matrix-vector equation approach
zbMATH Keywords: matrix equation approach
zbMATH Keywords: condition numbers
zbMATH Keywords: partial pivoting
zbMATH Keywords: sensitivity
zbMATH Keywords: \(LU\)-factorization
reviewed by: Florica Luban
describes a project that uses: mctoolbox
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02510255
OpenAlex ID: W2050250211
description: scientific article; zbMATH DE number 1228550