Existence test for solution of nonlinear systems applying affine arithmetic
type: Item
instance of: scholarly article
title: Existence test for solution of nonlinear systems applying affine arithmetic
zbMATH Open document ID: 1117.65075
author: Shinya Miyajima
author: Masahide Kashiwagi
published in: Journal of Computational and Applied Mathematics
publication date: 2007-02-02T00:00:00Z
review text: Given a continuous differentiable function \(f: \mathbb{R}^m\to\mathbb{R}^m\) and an \(m\)-dimensional interval vector \(X\) criteria are derived for verifying the existence of a zero \(x^*\in X\) of \(f\). Moreover, subsets of \(X\) can be given which do not contain a zero of \(f\). The criteria are based on affine arithmetic and Brouwer's fixed point theorem. A new test for existence and uniqueness of a zero of \(f\) is listed, many references for additional tests are given. Two numerical examples compare some of them with the new one showing that the latter succeeds in a shorter time than the other ones.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 65G20
zbMATH DE Number: 5121424
zbMATH Keywords: interval analysis
zbMATH Keywords: existence and uniqueness test
zbMATH Keywords: Krawczyk operator
zbMATH Keywords: Hansen operator
zbMATH Keywords: numerical examples
reviewed by: Günter Mayer
MaRDI profile type: Publication
full work available at URL: j.cam.2005.08.051
OpenAlex ID: W2095240851
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DOI: 10.1016/J.CAM.2005.08.051
description: scientific article; zbMATH DE number 5121424