On the applicability of the interval Gaussian algorithm
type: Item
instance of: scholarly article
title: On the applicability of the interval Gaussian algorithm
zbMATH Open document ID: 0933.65027
DOI: 10.1023/A:1009997411503
published in: Reliable Computing
publication date: 1999-01-17T00:00:00Z
review text: Let a system of linear interval equations, \(Ax =b\), be given where \(A\) is of the special form \(A= I +[-R,R]\) and regular, \(I\) is the identity matrix and \(R\) is a matrix with nonnegative real entries. The application of the interval Newton algorithm is investigated. The authors call the algorithm applicable to the system if no division through zero occurs during the computation so that a finite solution \(x_G\) is obtained. Now, necessary and sufficient conditions for the system are derived that the algorithm is applicable. Then it is shown that each component of \(x_G\), which is an interval vector has an endpoint which is optimum.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 1240636
zbMATH Keywords: interval Gaussian algorithm
zbMATH Keywords: system of linear interval equations
zbMATH Keywords: interval Newton algorithm
author: Günter Mayer
author: Jiří Rohn
reviewed by: H. Ratschek
MaRDI profile type: Publication
full work available at URL: a:1009997411503
OpenAlex ID: W33808975
description: scientific article; zbMATH DE number 1240636