A Sherman-Morrison approach to the solution of linear systems
type: Item
instance of: scholarly article
title: A Sherman-Morrison approach to the solution of linear systems
zbMATH Open document ID: 1090.65037
author: P. Maponi
author: N. Egidi
published in: Journal of Computational and Applied Mathematics
publication date: 2006-03-24T00:00:00Z
review text: An algorithm is proposed to solve a linear system \(Ax=b\) (\(A\in{\mathbb R}^{n\times n}\)) by writing \(A=A_0+P_1+\cdots+P_n\) where \(A_0=\text{diag}(A)\) and \(P_k\) is the rank one matrix that adds the off diagonal elements in the \(k\)th row of \(A\). First \(A_0 x_0 = b\) is solved, and then this solution is updated as implied by the Sherman-Morrison inversion formula for the \(n\) rank one modifications \(P_k\). The complexity is comparable to Gaussian elimination. When some pivoting strategy is implemented, also the accuracy is similar to Gaussian elimination with partial pivoting.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 5015163
zbMATH Keywords: direct method
zbMATH Keywords: matrix inverse
zbMATH Keywords: comparison of methods
zbMATH Keywords: algorithm
zbMATH Keywords: Sherman-Morrison inversion formula
zbMATH Keywords: complexity
zbMATH Keywords: Gaussian elimination
zbMATH Keywords: pivoting strategy
reviewed by: Adhemar Bultheel
describes a project that uses: NAG
describes a project that uses: nag
MaRDI profile type: Publication
full work available at URL: j.cam.2005.02.013
OpenAlex ID: W2078778009
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DOI: 10.1016/J.CAM.2005.02.013
description: scientific article; zbMATH DE number 5015163