Rehabilitation of the Gauss-Jordan algorithm
type: Item
instance of: scholarly article
title: Rehabilitation of the Gauss-Jordan algorithm
zbMATH Open document ID: 0672.65011
DOI: 10.1007/BF01396364
author: T. J. Dekker
author: Walter Hoffmann
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133335
review text: By using vector and parallel computers, a number of algorithms may have a renewed interest. In this paper, the Gauss-Jordan algorithm with column interchanges is analyzed. It is shown that by using the Gauss-Jordan algorithm with column interchanges, a more satisfactory bound for the residual norm can be given. The presented error analysis gives a theoretical evidence that this algorithm yields numerical solutions as good as those obtained by Gauss elimination. Furthermore, the residual of the obtained solution is not larger than that corresponding to the Gauss elimination's solution. For demonstrating that the error and the residual are satisfactory, some computer results are presented. Some results of experiments on a Cyber 205 vector computer are gathered to show that the Gauss-Jordan algorithm is not slower than the Gauss elimination for systems of order up to 25, although for its realization, about 1,5 times work is required.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65G50
Mathematics Subject Classification ID: 15A06
zbMATH DE Number: 4100478
zbMATH Keywords: vector and parallel computers
zbMATH Keywords: Gauss-Jordan algorithm
zbMATH Keywords: error analysis
zbMATH Keywords: Gauss elimination
zbMATH Keywords: computer results
describes a project that uses: LINPACK
describes a project that uses: NUMVEC
MaRDI profile type: Publication
cites work: Monitoring the numerical stability of Gaussian elimination
cites work: Q3932291
cites work: Q5185900
cites work: Solving linear systems on a vector computer
cites work: On the stability of Gauss-Jordan elimination with pivoting
cites work: Q4057472
description: scientific article; zbMATH DE number 4100478