Interval algorithm for absolute value equations
type: Item
instance of: scholarly article
title: Interval algorithm for absolute value equations
zbMATH Open document ID: 1236.65047
author: Aixiang Wang
author: Yongkun Deng
author: Hai-Jun Wang
published in: Central European Journal of Mathematics
publication date: 2012-01-16T00:00:00Z
review text: The authors consider the absolute value equation \(f(x):= Ax-|x|- b= 0\), \(A\in\mathbb{R}^{n\times n}\), \(b\in\mathbb{R}^n\). They present a generalized Newton method in order to approximate a zero \(x^*\) of \(f\). To this end they use a particular smoothing function \(f_\mu\) for \(f\). With a second algorithm they construct an enclosure of \(x^*\) using interval arithmetical tools, among them the so-called \(\varepsilon\)-inflation. Numerical experiments illustrate the efficiency of both methods.
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 15A06
zbMATH DE Number: 5997997
zbMATH Keywords: absolute value equation
zbMATH Keywords: generalized Newton method
zbMATH Keywords: \(\varepsilon\)-inflation
zbMATH Keywords: interval iteration
zbMATH Keywords: error estimation
zbMATH Keywords: linear complementarity problem
reviewed by: M. Milla Miranda
describes a project that uses: INTLAB
MaRDI profile type: Publication
full work available at URL: s11533-011-0067-2
OpenAlex ID: W2084109373
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DOI: 10.2478/S11533-011-0067-2
description: scientific article; zbMATH DE number 5997997