The solution of a type of absolute value equations using two new matrix splitting iterative techniques
Finding the solution of an absolute value vector equation (AVE) of the form Ax-\vert x\vert= b is an important subject in scientific computing, operations research, engineering, management science, and economic applications. This paper proposes two new iterative techniques to solve such AVEs. Both t...
Saved in:
| Published in | Portugaliae mathematica Vol. 79; no. 3; pp. 241 - 252 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
European Mathematical Society Publishing House
01.01.2022
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0032-5155 1662-2758 1662-2758 |
| DOI | 10.4171/pm/2089 |
Cover
| Abstract | Finding the solution of an absolute value vector equation (AVE) of the form
Ax-\vert x\vert= b
is an important subject in scientific computing, operations research, engineering, management science, and economic applications. This paper proposes two new iterative techniques to solve such AVEs. Both techniques are based on a decomposition of the coefficient matrix and a fixed-point principle. The convergence of the proposed techniques under appropriate assumptions is examined. We present results of numerical simulations to verify our theoretical findings and demonstrate the efficiency of our techniques. |
|---|---|
| AbstractList | Finding the solution of an absolute value vector equation (AVE) of the form Ax - |x| = b is an important subject in scientific computing, operations research, engineering, management science, and economic applications. This paper proposes two new iterative techniques to solve such AVEs. Both techniques are based on a decomposition of the coefficient matrix and a fixed-point principle. The convergence of the proposed techniques under appropriate assumptions is examined. We present results of numerical simulations to verify our theoretical findings and demonstrate the efficiency of our techniques. Finding the solution of an absolute value vector equation (AVE) of the form Ax-\vert x\vert= b is an important subject in scientific computing, operations research, engineering, management science, and economic applications. This paper proposes two new iterative techniques to solve such AVEs. Both techniques are based on a decomposition of the coefficient matrix and a fixed-point principle. The convergence of the proposed techniques under appropriate assumptions is examined. We present results of numerical simulations to verify our theoretical findings and demonstrate the efficiency of our techniques. |
| Audience | Academic |
| Author | Ali, Rashid Pan, Kejia |
| Author_xml | – sequence: 1 givenname: Rashid surname: Ali fullname: Ali, Rashid – sequence: 2 givenname: Kejia surname: Pan fullname: Pan, Kejia |
| BookMark | eNp1kE1vwjAMhqOJSQM27S_ktl0K-SBpe0RoXxLSLuxcpakDmdIPmhTGv18LO02bfLBlP69tvRM0quoKELqnZLagMZ035ZyRJL1CYyoli1gskhEaE8JZJKgQN2ji_SchjMtUjpHZ7AD72nXB1hWuDVY4nBo4V_m5D_igXAcY9p0aII87b6stDscaV3DEpQqt_cK-cTaEYWADtD15ABxA7yq778DfomujnIe7nzxFH89Pm9VrtH5_eVst15FmaRwiZqimAHGcFozHAEakVJiFFIXkoA3XxDBudE5jSYsip1SnXJo01YrncZEzPkWPl71d1ajTUTmXNa0tVXvKKMkGf7KmzAZ_enR2QbfKQWYrU4dW6T4KKK3uPTW27y8TlnAmhCS9ILoIdFt734LJtA1nS3qhdX8cePjF__fKN81xiaI |
| CitedBy_id | crossref_primary_10_1016_j_heliyon_2024_e34505 crossref_primary_10_1108_EC_11_2023_0781 |
| ContentType | Journal Article |
| Copyright | COPYRIGHT 2022 European Mathematical Society Publishing House |
| Copyright_xml | – notice: COPYRIGHT 2022 European Mathematical Society Publishing House |
| DBID | AAYXX CITATION ADTOC UNPAY |
| DOI | 10.4171/pm/2089 |
| DatabaseName | CrossRef Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1662-2758 |
| EndPage | 252 |
| ExternalDocumentID | 10.4171/pm/2089 A828325560 10_4171_pm_2089 |
| GeographicLocations | China |
| GeographicLocations_xml | – name: China |
| GroupedDBID | --Z -~X 9I1 AAYXX ABCQX ACIPV ACNCT AENEX AKZPS ALMA_UNASSIGNED_HOLDINGS AMVHM AUREJ CITATION E3Z EBS EJD FAEIB FEDTE FRJ FRP GROUPED_DOAJ H13 HVGLF IAO L7B OK1 P2P REM REW TN5 VH7 YNT -~9 2WC ABDSD ADTOC AFFNX ITC LO0 UNPAY |
| ID | FETCH-LOGICAL-c297t-2f1c1ee779d237eef5915f465d63ecf3c0f23fcb1761ddb11c936f99ca3b7db23 |
| IEDL.DBID | UNPAY |
| ISSN | 0032-5155 1662-2758 |
| IngestDate | Mon Sep 15 10:13:58 EDT 2025 Tue Jun 10 21:08:38 EDT 2025 Wed Oct 01 05:14:33 EDT 2025 Thu Apr 24 22:53:18 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| License | cc-by |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c297t-2f1c1ee779d237eef5915f465d63ecf3c0f23fcb1761ddb11c936f99ca3b7db23 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://doi.org/10.4171/pm/2089 |
| PageCount | 12 |
| ParticipantIDs | unpaywall_primary_10_4171_pm_2089 gale_infotracacademiconefile_A828325560 crossref_citationtrail_10_4171_pm_2089 crossref_primary_10_4171_pm_2089 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2022-01-01 |
| PublicationDateYYYYMMDD | 2022-01-01 |
| PublicationDate_xml | – month: 01 year: 2022 text: 2022-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Portugaliae mathematica |
| PublicationYear | 2022 |
| Publisher | European Mathematical Society Publishing House |
| Publisher_xml | – name: European Mathematical Society Publishing House |
| SSID | ssj0023696 |
| Score | 2.2343993 |
| Snippet | Finding the solution of an absolute value vector equation (AVE) of the form
Ax-\vert x\vert= b
is an important subject in scientific computing, operations... Finding the solution of an absolute value vector equation (AVE) of the form Ax - |x| = b is an important subject in scientific computing, operations research,... |
| SourceID | unpaywall gale crossref |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database |
| StartPage | 241 |
| SubjectTerms | Absolute value Fixed point theory Iterative methods (Mathematics) Matrices |
| Title | The solution of a type of absolute value equations using two new matrix splitting iterative techniques |
| URI | https://doi.org/10.4171/pm/2089 |
| UnpaywallVersion | publishedVersion |
| Volume | 79 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1662-2758 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0023696 issn: 1662-2758 databaseCode: DOA dateStart: 20220101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVEBS databaseName: EBSCOhost Mathematics Source - HOST customDbUrl: eissn: 1662-2758 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023696 issn: 1662-2758 databaseCode: AMVHM dateStart: 20151001 isFulltext: true titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source providerName: EBSCOhost |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT8MwDLbGdgAOvBHjMYKE4NSxNE26HifENCFt4sCkcaqa1OHAXrBOA349SduNAQJxqyo3imw3fsT-DHAuY4aKcc9BbbNVNSUcqWvKiZg2xiqWNUxTF-2OaHW92x7vFeB03guzdH_vUZ9ejQcmPK8HK1AS3DjbRSh1O3eNhwxs0YRRNJ1rSoWwTSa8nrXFLn_5xd7kp-7qdDiO3mZRv79kS5qbn1gCWQnJU3WayKp6_wbQ-Mc2t2Aj9yNJIxP8NhRwuAPr7QUI62QXtFEBMlctMtIkIjbhmj7J9D0Si_WNBJ8zwO8JsWXwjySZjYhxt8nA4ve_kolxVNPyaJJhMJsDkiywXyd70G3e3F-3nHysgqPcwE8cV1NFEX0_iF3mI2oeUK49wWNh5KaZqmmXaSWpL2gcS0pVwIQOAhUx6cfSZftQHI6GeAAk0hQVBsg826CKXJpYWzMuMUaNJtAsw8Wc-aHKMcft6It-aGIPy7hwPAgt48pAFoTjDGbjJ8mllV5ofzyzhory_gGzEwthFTbqduoSNx5cGc4WAv5ttcN_0BzBmmubHdKEyzEUk5cpnhgXJJGVNHSv5Mr4AZKm3N8 |
| linkProvider | Unpaywall |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT8MwDLZgOwAH3ojxDBKCU8fSNOl6nBDThLSJA5PGqWpShwN7QTsN-PUkbTcGCMStqtwost34EfszwLmMGSrGPQe1zVbVlHCkriknYtoYq1jWMEtdtDui1fVue7y3BKezXpiF-3uP-vRqPDDheT1YhrLgxtkuQbnbuWs85GCLJoyi2VxTKoRtMuH1vC128csv9qY4dVcmw3H0No36_QVb0tz4xBLIS0ieqpNUVtX7N4DGP7a5CeuFH0kaueC3YAmH27DWnoOwJjugjQqQmWqRkSYRsQnX7Elm75FYrG8k-JwDfifElsE_knQ6IsbdJgOL3_9KEuOoZuXRJMdgNgckmWO_JrvQbd7cX7ecYqyCo9zATx1XU0URfT-IXeYjah5Qrj3BY2HkppmqaZdpJakvaBxLSlXAhA4CFTHpx9Jle1Aajoa4DyTSFBUGyDzboIpcmlhbMy4xRo0m0KzAxYz5oSowx-3oi35oYg_LuHA8CC3jKkDmhOMcZuMnyaWVXmh_PLOGior-AbMTC2EVNup26hI3HlwFzuYC_m21g3_QHMKqa5sdsoTLEZTSlwkeGxcklSeFGn4Aauzb6g |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+solution+of+a+type+of+absolute+value+equations+using+two+new+matrix+splitting+iterative+techniques&rft.jtitle=Portugaliae+mathematica&rft.au=Ali%2C+Rashid&rft.au=Pan%2C+Kejia&rft.date=2022-01-01&rft.pub=European+Mathematical+Society+Publishing+House&rft.issn=0032-5155&rft.volume=79&rft.issue=3&rft.spage=241&rft_id=info:doi/10.4171%2FPM%2F2089&rft.externalDocID=A828325560 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0032-5155&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0032-5155&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0032-5155&client=summon |