{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:48:17Z","timestamp":1747190897022,"version":"3.40.5"},"reference-count":37,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T00:00:00Z","timestamp":1651795200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods"],"published-print":{"date-parts":[[2022,5,6]]},"abstract":"<jats:p>In this paper, we provide two new generalized Gauss-Seidel (NGGS) iteration methods for solving absolute value equations <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi>A<\/a:mi>\n                        <a:mi>x<\/a:mi>\n                        <a:mo>\u2212<\/a:mo>\n                        <a:mo>\u2223<\/a:mo>\n                        <a:mi>x<\/a:mi>\n                        <a:mo>\u2223<\/a:mo>\n                        <a:mo>=<\/a:mo>\n                        <a:mi>b<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula>, where <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <c:mi>A<\/c:mi>\n                        <c:mo>\u2208<\/c:mo>\n                        <c:msup>\n                           <c:mrow>\n                              <c:mi>R<\/c:mi>\n                           <\/c:mrow>\n                           <c:mrow>\n                              <c:mi>n<\/c:mi>\n                              <c:mo>\u00d7<\/c:mo>\n                              <c:mi>n<\/c:mi>\n                           <\/c:mrow>\n                        <\/c:msup>\n                     <\/c:math>\n                  <\/jats:inline-formula>, <jats:inline-formula>\n                     <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <e:mi>b<\/e:mi>\n                        <e:mo>\u2208<\/e:mo>\n                        <e:msup>\n                           <e:mrow>\n                              <e:mi>R<\/e:mi>\n                           <\/e:mrow>\n                           <e:mrow>\n                              <e:mi>n<\/e:mi>\n                           <\/e:mrow>\n                        <\/e:msup>\n                     <\/e:math>\n                  <\/jats:inline-formula>, and <jats:inline-formula>\n                     <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <g:mi>x<\/g:mi>\n                        <g:mo>\u2208<\/g:mo>\n                        <g:msup>\n                           <g:mrow>\n                              <g:mi>R<\/g:mi>\n                           <\/g:mrow>\n                           <g:mrow>\n                              <g:mi>n<\/g:mi>\n                           <\/g:mrow>\n                        <\/g:msup>\n                     <\/g:math>\n                  <\/jats:inline-formula> are unknown solution vectors. Also, convergence results are established under mild assumptions. Eventually, numerical results prove the credibility of our approaches.<\/jats:p>","DOI":"10.1155\/2022\/4266576","type":"journal-article","created":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T20:35:42Z","timestamp":1651869342000},"page":"1-7","source":"Crossref","is-referenced-by-count":3,"title":["The Solution of Absolute Value Equations Using Two New Generalized Gauss-Seidel Iteration Methods"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6240-7805","authenticated-orcid":true,"given":"Rashid","family":"Ali","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083 Hunan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.cam.2017.06.019","article-title":"Solving absolute value equation using complementarity and smoothing functions","volume":"327","author":"L. 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