{"title":"The Solution of Absolute Value Equations Using Two New Generalized Gauss-Seidel Iteration Methods","authors":"Rashid Ali","doi":"10.1155/2022/4266576","DOIUrl":null,"url":null,"abstract":"<div>\n <p>In this paper, we provide two new generalized Gauss-Seidel (NGGS) iteration methods for solving absolute value equations <i>A</i><i>x</i> − ∣<i>x</i> | = <i>b</i>, where <i>A</i> ∈ <i>R</i><sup><i>n</i>×<i>n</i></sup>, <i>b</i> ∈ <i>R</i><sup><i>n</i></sup>, and <i>x</i> ∈ <i>R</i><sup><i>n</i></sup> are unknown solution vectors. Also, convergence results are established under mild assumptions. Eventually, numerical results prove the credibility of our approaches.</p>\n </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/4266576","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Mathematical Methods","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2022/4266576","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, we provide two new generalized Gauss-Seidel (NGGS) iteration methods for solving absolute value equations Ax − ∣x | = b, where A ∈ Rn×n, b ∈ Rn, and x ∈ Rn are unknown solution vectors. Also, convergence results are established under mild assumptions. Eventually, numerical results prove the credibility of our approaches.
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