Three-step alternating iterations for index 1 and non-singular matrices
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article, we introduce a new iteration scheme called three-step altern...
Gespeichert in:
| Veröffentlicht in: | Numerical algorithms 2020-06, Vol.84 (2), p.457-483 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 483 |
|---|---|
| container_issue | 2 |
| container_start_page | 457 |
| container_title | Numerical algorithms |
| container_volume | 84 |
| creator | Nandi, Ashish Kumar Sahoo, Jajati Keshari Mishra, Debasisha |
| description | Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article, we introduce a new iteration scheme called three-step alternating iterations using proper splittings and group inverses to find an approximate solution of singular linear systems, iteratively. As a special case, the same findings also work for finding an approximate solution of non-singular linear systems. A preconditioned alternating iterative scheme is also proposed to relax some sufficient conditions and to obtain faster convergence as well. We then show that our scheme converges faster than the unpreconditioned one. The theoretical findings are then validated numerically. |
| doi_str_mv | 10.1007/s11075-019-00764-0 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2918492308</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2918492308</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-3fe1d9c8bb78fa23414da18d8934ea457ddb3d98dc40862246eae70eb4cb94fe3</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKt_wFPAc3TysZvkKEWrUPBSzyG7ma1b2mxNtqD_3ugK3jzNO_C8w_AQcs3hlgPou8w56IoBt6ystWJwQma80oJZUVenJQPXjEtrzslFzluAUhN6Rpbrt4TI8ogH6ncjpujHPm5oX2JJQ8y0GxLtY8APyqmPgcYhslyY484nuvdj6lvMl-Ss87uMV79zTl4fH9aLJ7Z6WT4v7lesFRpGJjvkwbamabTpvJCKq-C5CcZKhV5VOoRGBmtCq8DUQqgaPWrARrWNVR3KObmZ7h7S8H7EPLrtcCxP77ITlhtlhQRTKDFRbRpyTti5Q-r3Pn06Du5bmJuEuSLM_QhzUEpyKuUCxw2mv9P_tL4A6IRuVg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2918492308</pqid></control><display><type>article</type><title>Three-step alternating iterations for index 1 and non-singular matrices</title><source>SpringerNature Journals</source><creator>Nandi, Ashish Kumar ; Sahoo, Jajati Keshari ; Mishra, Debasisha</creator><creatorcontrib>Nandi, Ashish Kumar ; Sahoo, Jajati Keshari ; Mishra, Debasisha</creatorcontrib><description>Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article, we introduce a new iteration scheme called three-step alternating iterations using proper splittings and group inverses to find an approximate solution of singular linear systems, iteratively. As a special case, the same findings also work for finding an approximate solution of non-singular linear systems. A preconditioned alternating iterative scheme is also proposed to relax some sufficient conditions and to obtain faster convergence as well. We then show that our scheme converges faster than the unpreconditioned one. The theoretical findings are then validated numerically.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-019-00764-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Computer Science ; Convergence ; Euclidean space ; Growth models ; Iterative methods ; Linear systems ; Markov analysis ; Mathematical analysis ; Numeric Computing ; Numerical Analysis ; Original Paper ; Partial differential equations ; Theory of Computation</subject><ispartof>Numerical algorithms, 2020-06, Vol.84 (2), p.457-483</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-3fe1d9c8bb78fa23414da18d8934ea457ddb3d98dc40862246eae70eb4cb94fe3</cites><orcidid>0000-0001-7162-1873</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11075-019-00764-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11075-019-00764-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Nandi, Ashish Kumar</creatorcontrib><creatorcontrib>Sahoo, Jajati Keshari</creatorcontrib><creatorcontrib>Mishra, Debasisha</creatorcontrib><title>Three-step alternating iterations for index 1 and non-singular matrices</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><description>Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article, we introduce a new iteration scheme called three-step alternating iterations using proper splittings and group inverses to find an approximate solution of singular linear systems, iteratively. As a special case, the same findings also work for finding an approximate solution of non-singular linear systems. A preconditioned alternating iterative scheme is also proposed to relax some sufficient conditions and to obtain faster convergence as well. We then show that our scheme converges faster than the unpreconditioned one. The theoretical findings are then validated numerically.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computer Science</subject><subject>Convergence</subject><subject>Euclidean space</subject><subject>Growth models</subject><subject>Iterative methods</subject><subject>Linear systems</subject><subject>Markov analysis</subject><subject>Mathematical analysis</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Partial differential equations</subject><subject>Theory of Computation</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1LAzEQhoMoWKt_wFPAc3TysZvkKEWrUPBSzyG7ma1b2mxNtqD_3ugK3jzNO_C8w_AQcs3hlgPou8w56IoBt6ystWJwQma80oJZUVenJQPXjEtrzslFzluAUhN6Rpbrt4TI8ogH6ncjpujHPm5oX2JJQ8y0GxLtY8APyqmPgcYhslyY484nuvdj6lvMl-Ss87uMV79zTl4fH9aLJ7Z6WT4v7lesFRpGJjvkwbamabTpvJCKq-C5CcZKhV5VOoRGBmtCq8DUQqgaPWrARrWNVR3KObmZ7h7S8H7EPLrtcCxP77ITlhtlhQRTKDFRbRpyTti5Q-r3Pn06Du5bmJuEuSLM_QhzUEpyKuUCxw2mv9P_tL4A6IRuVg</recordid><startdate>20200601</startdate><enddate>20200601</enddate><creator>Nandi, Ashish Kumar</creator><creator>Sahoo, Jajati Keshari</creator><creator>Mishra, Debasisha</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0001-7162-1873</orcidid></search><sort><creationdate>20200601</creationdate><title>Three-step alternating iterations for index 1 and non-singular matrices</title><author>Nandi, Ashish Kumar ; Sahoo, Jajati Keshari ; Mishra, Debasisha</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-3fe1d9c8bb78fa23414da18d8934ea457ddb3d98dc40862246eae70eb4cb94fe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Computer Science</topic><topic>Convergence</topic><topic>Euclidean space</topic><topic>Growth models</topic><topic>Iterative methods</topic><topic>Linear systems</topic><topic>Markov analysis</topic><topic>Mathematical analysis</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Partial differential equations</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nandi, Ashish Kumar</creatorcontrib><creatorcontrib>Sahoo, Jajati Keshari</creatorcontrib><creatorcontrib>Mishra, Debasisha</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nandi, Ashish Kumar</au><au>Sahoo, Jajati Keshari</au><au>Mishra, Debasisha</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Three-step alternating iterations for index 1 and non-singular matrices</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2020-06-01</date><risdate>2020</risdate><volume>84</volume><issue>2</issue><spage>457</spage><epage>483</epage><pages>457-483</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article, we introduce a new iteration scheme called three-step alternating iterations using proper splittings and group inverses to find an approximate solution of singular linear systems, iteratively. As a special case, the same findings also work for finding an approximate solution of non-singular linear systems. A preconditioned alternating iterative scheme is also proposed to relax some sufficient conditions and to obtain faster convergence as well. We then show that our scheme converges faster than the unpreconditioned one. The theoretical findings are then validated numerically.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11075-019-00764-0</doi><tpages>27</tpages><orcidid>https://orcid.org/0000-0001-7162-1873</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1017-1398 |
| ispartof | Numerical algorithms, 2020-06, Vol.84 (2), p.457-483 |
| issn | 1017-1398 1572-9265 |
| language | eng |
| recordid | cdi_proquest_journals_2918492308 |
| source | SpringerNature Journals |
| subjects | Algebra Algorithms Computer Science Convergence Euclidean space Growth models Iterative methods Linear systems Markov analysis Mathematical analysis Numeric Computing Numerical Analysis Original Paper Partial differential equations Theory of Computation |
| title | Three-step alternating iterations for index 1 and non-singular matrices |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-23T03%3A47%3A04IST&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=Three-step%20alternating%20iterations%20for%20index%201%20and%20non-singular%20matrices&rft.jtitle=Numerical%20algorithms&rft.au=Nandi,%20Ashish%20Kumar&rft.date=2020-06-01&rft.volume=84&rft.issue=2&rft.spage=457&rft.epage=483&rft.pages=457-483&rft.issn=1017-1398&rft.eissn=1572-9265&rft_id=info:doi/10.1007/s11075-019-00764-0&rft_dat=%3Cproquest_cross%3E2918492308%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=2918492308&rft_id=info:pmid/&rfr_iscdi=true |