Optimally conditioned scaled ABS algorithms for linear systems
type: Item
instance of: scholarly article
title: Optimally conditioned scaled ABS algorithms for linear systems
zbMATH Open document ID: 0688.65026
DOI: 10.1007/BF00939740
author: K. Appert
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: Using a strict bound of the first author to the condition number of bordered positive-definite matrices, we show that the scaling parameter in the ABS class for linear systems can always be chosen so that the bound of a certain update matrix is globally minimized. Moreover, if the scaling parameter is so chosen at every iteration, then the condition number itself is globally minimized. The resulting class of optimally conditioned algorithms contains as a special case the class of optimally stable algorithms in the sense of Broyden.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 4128298
zbMATH Keywords: Abaffy-Broyden-Spedicato algorithm
zbMATH Keywords: ABS algorithms
zbMATH Keywords: optimal conditioning
zbMATH Keywords: optimal stability
zbMATH Keywords: condition number
zbMATH Keywords: bordered positive-definite matrices
zbMATH Keywords: scaling parameter
MaRDI profile type: Publication
cites work: A class of direct methods for linear systems
cites work: Q3805750
cites work: Q3995754
cites work: A direct method for the general solution of a system of linear equations
cites work: Numerical experiments with the symmetric algorithm in the ABS class for linear systems
cites work: On the numerical stability of Huang's update
cites work: On the numerical stability of Huang's and related methods
cites work: Variationally derived algorithms in the ABS class for linear systems
cites work: A strict bound to the condition number of bordered positive definite matrices
description: scientific article; zbMATH DE number 4128298