A new method based on generalized Taylor expansion for computing a series solution of the linear systems
In this paper, based on the generalized Taylor expansion and using the iteration matrix G of the iterative methods, we introduce a new method for computing a series solution of the linear systems. This method can be used to accelerate the convergence of the basic iterative methods. In addition, we s...
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Veröffentlicht in: | Applied mathematics and computation 2014-12, Vol.248, p.602-609 |
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description | In this paper, based on the generalized Taylor expansion and using the iteration matrix G of the iterative methods, we introduce a new method for computing a series solution of the linear systems. This method can be used to accelerate the convergence of the basic iterative methods. In addition, we show that, by applying the new method to a divergent iterative scheme, it is possible to construct a convergent series solution and to find the convergence intervals of control parameter for special cases. Numerical experiments are given to show the efficiency of the new method. |
doi_str_mv | 10.1016/j.amc.2014.10.003 |
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Numerical experiments are given to show the efficiency of the new method.</description><identifier>ISSN: 0096-3003</identifier><identifier>EISSN: 1873-5649</identifier><identifier>DOI: 10.1016/j.amc.2014.10.003</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Basic iterative method ; Computation ; Construction ; Convergence ; Generalized Taylor expansion ; Intervals ; Iterative methods ; Linear system ; Linear systems ; Mathematical analysis ; Mathematical models ; Spectral radius</subject><ispartof>Applied mathematics and computation, 2014-12, Vol.248, p.602-609</ispartof><rights>2014 Elsevier Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c330t-871db651e168c91ac6f23daca2bb0cec6166f7abae1255fa18afcb882e3b3d8d3</citedby><cites>FETCH-LOGICAL-c330t-871db651e168c91ac6f23daca2bb0cec6166f7abae1255fa18afcb882e3b3d8d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.amc.2014.10.003$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>315,781,785,3551,27929,27930,46000</link.rule.ids></links><search><creatorcontrib>Toutounian, F.</creatorcontrib><creatorcontrib>Nasabzadeh, H.</creatorcontrib><title>A new method based on generalized Taylor expansion for computing a series solution of the linear systems</title><title>Applied mathematics and computation</title><description>In this paper, based on the generalized Taylor expansion and using the iteration matrix G of the iterative methods, we introduce a new method for computing a series solution of the linear systems. This method can be used to accelerate the convergence of the basic iterative methods. In addition, we show that, by applying the new method to a divergent iterative scheme, it is possible to construct a convergent series solution and to find the convergence intervals of control parameter for special cases. Numerical experiments are given to show the efficiency of the new method.</description><subject>Basic iterative method</subject><subject>Computation</subject><subject>Construction</subject><subject>Convergence</subject><subject>Generalized Taylor expansion</subject><subject>Intervals</subject><subject>Iterative methods</subject><subject>Linear system</subject><subject>Linear systems</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Spectral radius</subject><issn>0096-3003</issn><issn>1873-5649</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9UDtPwzAQthBIlMcPYPPIkuKLWycVU4V4SZVYymxdnEvrKomLLwXKr8dVmZlO31O6T4gbUGNQYO42Y-zcOFcwSXislD4RIygLnU3NZHYqRkrNTKYTfy4umDdKqcLAZCTWc9nTl-xoWIdaVshUy9DLFfUUsfU_CS5x34Yo6XuLPfskNgm50G13g-9XEiVT9MSSQ5uYpIdGDmuSre8Jo-Q9D9TxlThrsGW6_ruX4v3pcfnwki3enl8f5ovMaa2GrCygrswUCEzpZoDONLmu0WFeVcqRM2BMU2CFBPl02iCU2LiqLHPSla7LWl-K22PvNoaPHfFgO8-O2hZ7Cju2kMp1kU8MJCscrS4G5kiN3UbfYdxbUPawqt3YtKo9rHqg0nopc3_MUPrh01O07Dz1jmofyQ22Dv6f9C_89oHi</recordid><startdate>20141201</startdate><enddate>20141201</enddate><creator>Toutounian, F.</creator><creator>Nasabzadeh, H.</creator><general>Elsevier Inc</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></search><sort><creationdate>20141201</creationdate><title>A new method based on generalized Taylor expansion for computing a series solution of the linear systems</title><author>Toutounian, F. ; Nasabzadeh, H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c330t-871db651e168c91ac6f23daca2bb0cec6166f7abae1255fa18afcb882e3b3d8d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Basic iterative method</topic><topic>Computation</topic><topic>Construction</topic><topic>Convergence</topic><topic>Generalized Taylor expansion</topic><topic>Intervals</topic><topic>Iterative methods</topic><topic>Linear system</topic><topic>Linear systems</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Spectral radius</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Toutounian, F.</creatorcontrib><creatorcontrib>Nasabzadeh, H.</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>Applied mathematics and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Toutounian, F.</au><au>Nasabzadeh, H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new method based on generalized Taylor expansion for computing a series solution of the linear systems</atitle><jtitle>Applied mathematics and computation</jtitle><date>2014-12-01</date><risdate>2014</risdate><volume>248</volume><spage>602</spage><epage>609</epage><pages>602-609</pages><issn>0096-3003</issn><eissn>1873-5649</eissn><abstract>In this paper, based on the generalized Taylor expansion and using the iteration matrix G of the iterative methods, we introduce a new method for computing a series solution of the linear systems. 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subjects | Basic iterative method Computation Construction Convergence Generalized Taylor expansion Intervals Iterative methods Linear system Linear systems Mathematical analysis Mathematical models Spectral radius |
title | A new method based on generalized Taylor expansion for computing a series solution of the linear systems |
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