Accelerated iterative method for Z-matrices
It has recently been reported that the convergence of the preconditioned Gauss-Seidel method which uses a matrix of the type ( I + U) as a preconditioner is faster than the basic iterative method. In this paper, we generalize the preconditioner to the type ( I + βU), where β is a positive real numbe...
Gespeichert in:
| Veröffentlicht in: | Journal of computational and applied mathematics 1996-11, Vol.75 (1), p.87-97 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 97 |
|---|---|
| container_issue | 1 |
| container_start_page | 87 |
| container_title | Journal of computational and applied mathematics |
| container_volume | 75 |
| creator | Kotakemori, Hisashi Niki, Hiroshi Okamoto, Naotaka |
| description | It has recently been reported that the convergence of the preconditioned Gauss-Seidel method which uses a matrix of the type (
I +
U) as a preconditioner is faster than the basic iterative method. In this paper, we generalize the preconditioner to the type (
I +
βU), where β is a positive real number. After discussing convergence of the method applied to Z-matrices, we propose an algorithm for estimating the optimum
β. Numerical examples are also given, which show the effectiveness of our algorithm. |
| doi_str_mv | 10.1016/S0377-0427(96)00061-1 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_26083958</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377042796000611</els_id><sourcerecordid>26083958</sourcerecordid><originalsourceid>FETCH-LOGICAL-c433t-e92eaacb4355f2e62175e6d937ccf8b699cb96716c33a0809a13569ba858a53e3</originalsourceid><addsrcrecordid>eNqFkM1Lw0AQxRdRsFb_BCEHEUWiu9ns10lK8QsKHtSLl2UzmeBK0tTdtOB_b9KUXj3NHH5v3rxHyDmjt4wyefdGuVIpzTN1ZeQ1pVSylB2QCdPKpEwpfUgme-SYnMT4PUCG5RNyMwPAGoPrsEx8Nyx-g0mD3VdbJlUbks-0cV3wgPGUHFWujni2m1Py8fjwPn9OF69PL_PZIoWc8y5Fk6FzUORciCpDmTElUJaGK4BKF9IYKIxUTALnjmpqHONCmsJpoZ3gyKfkcry7Cu3PGmNnGx_7L2u3xHYdbSap5kboHhQjCKGNMWBlV8E3LvxaRu1Qjd1WY4fc1ki7rcayXnexM3ARXF0FtwQf9-JMUKPYgN2PGPZhNx6DjeBxCVj6gNDZsvX_GP0BE7N2Zw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>26083958</pqid></control><display><type>article</type><title>Accelerated iterative method for Z-matrices</title><source>Elsevier ScienceDirect Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Kotakemori, Hisashi ; Niki, Hiroshi ; Okamoto, Naotaka</creator><creatorcontrib>Kotakemori, Hisashi ; Niki, Hiroshi ; Okamoto, Naotaka</creatorcontrib><description>It has recently been reported that the convergence of the preconditioned Gauss-Seidel method which uses a matrix of the type (
I +
U) as a preconditioner is faster than the basic iterative method. In this paper, we generalize the preconditioner to the type (
I +
βU), where β is a positive real number. After discussing convergence of the method applied to Z-matrices, we propose an algorithm for estimating the optimum
β. Numerical examples are also given, which show the effectiveness of our algorithm.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/S0377-0427(96)00061-1</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Algebra ; Exact sciences and technology ; Gauss-Seidel method ; Linear and multilinear algebra, matrix theory ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical linear algebra ; Preconditioning ; Sciences and techniques of general use ; SOR method ; Z-matrix</subject><ispartof>Journal of computational and applied mathematics, 1996-11, Vol.75 (1), p.87-97</ispartof><rights>1996 Elsevier Science B.V. All rights reserved</rights><rights>1997 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c433t-e92eaacb4355f2e62175e6d937ccf8b699cb96716c33a0809a13569ba858a53e3</citedby><cites>FETCH-LOGICAL-c433t-e92eaacb4355f2e62175e6d937ccf8b699cb96716c33a0809a13569ba858a53e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0377042796000611$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2509711$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Kotakemori, Hisashi</creatorcontrib><creatorcontrib>Niki, Hiroshi</creatorcontrib><creatorcontrib>Okamoto, Naotaka</creatorcontrib><title>Accelerated iterative method for Z-matrices</title><title>Journal of computational and applied mathematics</title><description>It has recently been reported that the convergence of the preconditioned Gauss-Seidel method which uses a matrix of the type (
I +
U) as a preconditioner is faster than the basic iterative method. In this paper, we generalize the preconditioner to the type (
I +
βU), where β is a positive real number. After discussing convergence of the method applied to Z-matrices, we propose an algorithm for estimating the optimum
β. Numerical examples are also given, which show the effectiveness of our algorithm.</description><subject>Algebra</subject><subject>Exact sciences and technology</subject><subject>Gauss-Seidel method</subject><subject>Linear and multilinear algebra, matrix theory</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical linear algebra</subject><subject>Preconditioning</subject><subject>Sciences and techniques of general use</subject><subject>SOR method</subject><subject>Z-matrix</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNqFkM1Lw0AQxRdRsFb_BCEHEUWiu9ns10lK8QsKHtSLl2UzmeBK0tTdtOB_b9KUXj3NHH5v3rxHyDmjt4wyefdGuVIpzTN1ZeQ1pVSylB2QCdPKpEwpfUgme-SYnMT4PUCG5RNyMwPAGoPrsEx8Nyx-g0mD3VdbJlUbks-0cV3wgPGUHFWujni2m1Py8fjwPn9OF69PL_PZIoWc8y5Fk6FzUORciCpDmTElUJaGK4BKF9IYKIxUTALnjmpqHONCmsJpoZ3gyKfkcry7Cu3PGmNnGx_7L2u3xHYdbSap5kboHhQjCKGNMWBlV8E3LvxaRu1Qjd1WY4fc1ki7rcayXnexM3ARXF0FtwQf9-JMUKPYgN2PGPZhNx6DjeBxCVj6gNDZsvX_GP0BE7N2Zw</recordid><startdate>19961112</startdate><enddate>19961112</enddate><creator>Kotakemori, Hisashi</creator><creator>Niki, Hiroshi</creator><creator>Okamoto, Naotaka</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19961112</creationdate><title>Accelerated iterative method for Z-matrices</title><author>Kotakemori, Hisashi ; Niki, Hiroshi ; Okamoto, Naotaka</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c433t-e92eaacb4355f2e62175e6d937ccf8b699cb96716c33a0809a13569ba858a53e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>Algebra</topic><topic>Exact sciences and technology</topic><topic>Gauss-Seidel method</topic><topic>Linear and multilinear algebra, matrix theory</topic><topic>Mathematics</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Numerical linear algebra</topic><topic>Preconditioning</topic><topic>Sciences and techniques of general use</topic><topic>SOR method</topic><topic>Z-matrix</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kotakemori, Hisashi</creatorcontrib><creatorcontrib>Niki, Hiroshi</creatorcontrib><creatorcontrib>Okamoto, Naotaka</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kotakemori, Hisashi</au><au>Niki, Hiroshi</au><au>Okamoto, Naotaka</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Accelerated iterative method for Z-matrices</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>1996-11-12</date><risdate>1996</risdate><volume>75</volume><issue>1</issue><spage>87</spage><epage>97</epage><pages>87-97</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>It has recently been reported that the convergence of the preconditioned Gauss-Seidel method which uses a matrix of the type (
I +
U) as a preconditioner is faster than the basic iterative method. In this paper, we generalize the preconditioner to the type (
I +
βU), where β is a positive real number. After discussing convergence of the method applied to Z-matrices, we propose an algorithm for estimating the optimum
β. Numerical examples are also given, which show the effectiveness of our algorithm.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/S0377-0427(96)00061-1</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 1996-11, Vol.75 (1), p.87-97 |
| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_26083958 |
| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Algebra Exact sciences and technology Gauss-Seidel method Linear and multilinear algebra, matrix theory Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Preconditioning Sciences and techniques of general use SOR method Z-matrix |
| title | Accelerated iterative method for Z-matrices |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-10T18%3A42%3A27IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Accelerated%20iterative%20method%20for%20Z-matrices&rft.jtitle=Journal%20of%20computational%20and%20applied%20mathematics&rft.au=Kotakemori,%20Hisashi&rft.date=1996-11-12&rft.volume=75&rft.issue=1&rft.spage=87&rft.epage=97&rft.pages=87-97&rft.issn=0377-0427&rft.eissn=1879-1778&rft.coden=JCAMDI&rft_id=info:doi/10.1016/S0377-0427(96)00061-1&rft_dat=%3Cproquest_cross%3E26083958%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=26083958&rft_id=info:pmid/&rft_els_id=S0377042796000611&rfr_iscdi=true |