MDSS-based iteration method for weakly nonlinear systems with complex coefficient matrices
In this paper,we devote to improve an effective iterative method for solving weakly nonlinear systems with large sparse complex symmetric Jacobian matrix. Employing the Anderson mixing to speed up the convergence of double-step scale splitting (DSS) iteration, we establish a modified DSS (MDSS) iter...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2023-10, Vol.69 (5), p.3579-3600 |
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| container_title | Journal of applied mathematics & computing |
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| creator | Xiao, Yao Wu, Qingbiao Zhang, Yuanyuan |
| description | In this paper,we devote to improve an effective iterative method for solving weakly nonlinear systems with large sparse complex symmetric Jacobian matrix. Employing the Anderson mixing to speed up the convergence of double-step scale splitting (DSS) iteration, we establish a modified DSS (MDSS) iteration method for solving linear system with complex symmetric matrix. We propose the Picard-MDSS method based on the separability of linear and nonlinear terms by combining modified DSS (MDSS) methods of linear systems. We explore convergence theorems for the MDSS and Picard-MDSS methods under proper conditions. Furthermore, we conclude that our new methods are more efficient in comparison to several known methods through numerical experiments. The numerical results show the superiority of our new methods in CPU time and iteration steps. |
| doi_str_mv | 10.1007/s12190-023-01894-4 |
| format | Article |
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Employing the Anderson mixing to speed up the convergence of double-step scale splitting (DSS) iteration, we establish a modified DSS (MDSS) iteration method for solving linear system with complex symmetric matrix. We propose the Picard-MDSS method based on the separability of linear and nonlinear terms by combining modified DSS (MDSS) methods of linear systems. We explore convergence theorems for the MDSS and Picard-MDSS methods under proper conditions. Furthermore, we conclude that our new methods are more efficient in comparison to several known methods through numerical experiments. The numerical results show the superiority of our new methods in CPU time and iteration steps.</description><identifier>ISSN: 1598-5865</identifier><identifier>EISSN: 1865-2085</identifier><identifier>DOI: 10.1007/s12190-023-01894-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Computational Mathematics and Numerical Analysis ; Convergence ; Iterative methods ; Jacobi matrix method ; Jacobian matrix ; Linear systems ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Nonlinear systems ; Numerical methods ; Original Research ; System effectiveness ; Theory of Computation</subject><ispartof>Journal of applied mathematics & computing, 2023-10, Vol.69 (5), p.3579-3600</ispartof><rights>The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-6f499b1d22dba6e9417372ba2be0e384ec40da9afe352023a6dd89379fa8925f3</cites><orcidid>0000-0003-2706-6264</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/s12190-023-01894-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12190-023-01894-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Xiao, Yao</creatorcontrib><creatorcontrib>Wu, Qingbiao</creatorcontrib><creatorcontrib>Zhang, Yuanyuan</creatorcontrib><title>MDSS-based iteration method for weakly nonlinear systems with complex coefficient matrices</title><title>Journal of applied mathematics & computing</title><addtitle>J. Appl. Math. Comput</addtitle><description>In this paper,we devote to improve an effective iterative method for solving weakly nonlinear systems with large sparse complex symmetric Jacobian matrix. Employing the Anderson mixing to speed up the convergence of double-step scale splitting (DSS) iteration, we establish a modified DSS (MDSS) iteration method for solving linear system with complex symmetric matrix. We propose the Picard-MDSS method based on the separability of linear and nonlinear terms by combining modified DSS (MDSS) methods of linear systems. We explore convergence theorems for the MDSS and Picard-MDSS methods under proper conditions. Furthermore, we conclude that our new methods are more efficient in comparison to several known methods through numerical experiments. The numerical results show the superiority of our new methods in CPU time and iteration steps.</description><subject>Computational Mathematics and Numerical Analysis</subject><subject>Convergence</subject><subject>Iterative methods</subject><subject>Jacobi matrix method</subject><subject>Jacobian matrix</subject><subject>Linear systems</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Nonlinear systems</subject><subject>Numerical methods</subject><subject>Original Research</subject><subject>System effectiveness</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9ULtOwzAUtRBIlMIPMFliNthO4tgjKk-piKGwsFhOck1dkrjYRqV_j6FIbEzn6uo8dA5Cp4yeM0rri8g4U5RQXhDKpCpJuYcmTIqKcCqr_XxXSpIqPw7RUYwrSkWtqJqgl4erxYI0JkKHXYJgkvMjHiAtfYetD3gD5q3f4tGPvRvBBBy3McEQ8calJW79sO7hMyNY61oHY8KDScG1EI_RgTV9hJNfnKLnm-un2R2ZP97ezy7npOU1TUTYUqmGdZx3jRGgSlYXNW8Mb4BCIUtoS9oZZSwUFc8Fjeg6qYpaWSMVr2wxRWc733Xw7x8Qk175jzDmSM2lUKKqqWCZxXesNvgYA1i9Dm4wYasZ1d8b6t2GOkfonw11mUXFThQzeXyF8Gf9j-oLNmZ1gQ</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Xiao, Yao</creator><creator>Wu, Qingbiao</creator><creator>Zhang, Yuanyuan</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-2706-6264</orcidid></search><sort><creationdate>20231001</creationdate><title>MDSS-based iteration method for weakly nonlinear systems with complex coefficient matrices</title><author>Xiao, Yao ; Wu, Qingbiao ; Zhang, Yuanyuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-6f499b1d22dba6e9417372ba2be0e384ec40da9afe352023a6dd89379fa8925f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Computational Mathematics and Numerical Analysis</topic><topic>Convergence</topic><topic>Iterative methods</topic><topic>Jacobi matrix method</topic><topic>Jacobian matrix</topic><topic>Linear systems</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Nonlinear systems</topic><topic>Numerical methods</topic><topic>Original Research</topic><topic>System effectiveness</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xiao, Yao</creatorcontrib><creatorcontrib>Wu, Qingbiao</creatorcontrib><creatorcontrib>Zhang, Yuanyuan</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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 applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xiao, Yao</au><au>Wu, Qingbiao</au><au>Zhang, Yuanyuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>MDSS-based iteration method for weakly nonlinear systems with complex coefficient matrices</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. Appl. Math. Comput</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>69</volume><issue>5</issue><spage>3579</spage><epage>3600</epage><pages>3579-3600</pages><issn>1598-5865</issn><eissn>1865-2085</eissn><abstract>In this paper,we devote to improve an effective iterative method for solving weakly nonlinear systems with large sparse complex symmetric Jacobian matrix. Employing the Anderson mixing to speed up the convergence of double-step scale splitting (DSS) iteration, we establish a modified DSS (MDSS) iteration method for solving linear system with complex symmetric matrix. We propose the Picard-MDSS method based on the separability of linear and nonlinear terms by combining modified DSS (MDSS) methods of linear systems. We explore convergence theorems for the MDSS and Picard-MDSS methods under proper conditions. Furthermore, we conclude that our new methods are more efficient in comparison to several known methods through numerical experiments. 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| subjects | Computational Mathematics and Numerical Analysis Convergence Iterative methods Jacobi matrix method Jacobian matrix Linear systems Mathematical analysis Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Nonlinear systems Numerical methods Original Research System effectiveness Theory of Computation |
| title | MDSS-based iteration method for weakly nonlinear systems with complex coefficient matrices |
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