A verification method for enclosing solutions of absolute value equations
type: Item
instance of: scholarly article
title: A verification method for enclosing solutions of absolute value equations
zbMATH Open document ID: 1310.65057
author: Hao Liu
author: Suyu Cao
author: Hai-Jun Wang
published in: Collectanea Mathematica
publication date: 2013-03-27T00:00:00Z
review text: The authors consider the absolue value equations (AVE), \(Ax-|x| =b\), where \(A \in \mathbb{R}^{n \times n}\), and \(b \in \mathbb{R}^{n}\). Determining the existence of a solution is a NP-hard problem. The authors give a sufficient condition to guarantee that a given interval vector contains an exact solution of AVE. Their results are based on the use of interval arithmetic. Given an initial enclosure of a solution, they propose two new interval iterations that converge to that solution under mild assumptions. They also give some methods to compute an initial interval that contains a solution when the matrix \(A\) has some special properties. They also present some numerical experiments that confirm the power of their methods.
reviewed by: Stef Graillat
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 65G20
zbMATH DE Number: 6148951
zbMATH Keywords: absolute value equations
zbMATH Keywords: existence of solutions
zbMATH Keywords: enclose of solutions
zbMATH Keywords: \(H\)-matrix
zbMATH Keywords: interval arithmetic
zbMATH Keywords: interval iteration
zbMATH Keywords: numerical experiment
MaRDI profile type: Publication
full work available at URL: s13348-011-0057-5
OpenAlex ID: W2088306780
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DOI: 10.1007/S13348-011-0057-5
description: scientific article; zbMATH DE number 6148951