Solving systems of nonlinear equations In using a rotating hyperplane in
A procedure which accelerates the convergence of iterative methods for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in is introduced. This procedure uses a rotating hyperplane in , whose rotation axis depends on the current approximation n-1 of components...
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| Veröffentlicht in: | International journal of computer mathematics 1990-01, Vol.35 (1-4), p.133-151 |
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| container_end_page | 151 |
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| container_issue | 1-4 |
| container_start_page | 133 |
| container_title | International journal of computer mathematics |
| container_volume | 35 |
| creator | Grapsa, T.N. Vrahatis, M.N. Bountis, T.C. |
| description | A procedure which accelerates the convergence of iterative methods for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in
is introduced. This procedure uses a rotating hyperplane in
, whose rotation axis depends on the current approximation n-1 of components of the solution. The proposed procedure is applied here on the traditional Newton's method and on a recently proposed "dimension-reducing" method [5] which incorporates the advantages of nonlinear SOR and Newton's algorithms. In this way, two new modified schemes for solving nonlinear systems are correspondingly obtained. For both of these schemes proofs of convergence are given and numerical applications are presented. |
| doi_str_mv | 10.1080/00207169008803894 |
| format | Article |
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is introduced. This procedure uses a rotating hyperplane in
, whose rotation axis depends on the current approximation n-1 of components of the solution. The proposed procedure is applied here on the traditional Newton's method and on a recently proposed "dimension-reducing" method [5] which incorporates the advantages of nonlinear SOR and Newton's algorithms. In this way, two new modified schemes for solving nonlinear systems are correspondingly obtained. For both of these schemes proofs of convergence are given and numerical applications are presented.</description><identifier>ISSN: 0020-7160</identifier><identifier>EISSN: 1029-0265</identifier><identifier>DOI: 10.1080/00207169008803894</identifier><language>eng</language><publisher>Gordon and Breach Science Publishers</publisher><subject>bisection method ; dimension-reducing method ; G.1.5 ; implicit function theorem ; imprecise function values ; m-step SOR-Newton ; Newton's method ; nonlinear equations ; nonlinear SOR ; numerical solution ; quadratic convergence ; reduction to one-dimensional equations ; zeros</subject><ispartof>International journal of computer mathematics, 1990-01, Vol.35 (1-4), p.133-151</ispartof><rights>Copyright Taylor & Francis Group, LLC 1990</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c1434-2b341452ea5528ffab9a2b580cee25278dcb699255b73a9abee7bdcd84b658663</citedby><cites>FETCH-LOGICAL-c1434-2b341452ea5528ffab9a2b580cee25278dcb699255b73a9abee7bdcd84b658663</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/00207169008803894$$EPDF$$P50$$Ginformaworld$$H</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/00207169008803894$$EHTML$$P50$$Ginformaworld$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,59620,60409</link.rule.ids></links><search><creatorcontrib>Grapsa, T.N.</creatorcontrib><creatorcontrib>Vrahatis, M.N.</creatorcontrib><creatorcontrib>Bountis, T.C.</creatorcontrib><title>Solving systems of nonlinear equations In using a rotating hyperplane in</title><title>International journal of computer mathematics</title><description>A procedure which accelerates the convergence of iterative methods for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in
is introduced. This procedure uses a rotating hyperplane in
, whose rotation axis depends on the current approximation n-1 of components of the solution. The proposed procedure is applied here on the traditional Newton's method and on a recently proposed "dimension-reducing" method [5] which incorporates the advantages of nonlinear SOR and Newton's algorithms. In this way, two new modified schemes for solving nonlinear systems are correspondingly obtained. For both of these schemes proofs of convergence are given and numerical applications are presented.</description><subject>bisection method</subject><subject>dimension-reducing method</subject><subject>G.1.5</subject><subject>implicit function theorem</subject><subject>imprecise function values</subject><subject>m-step SOR-Newton</subject><subject>Newton's method</subject><subject>nonlinear equations</subject><subject>nonlinear SOR</subject><subject>numerical solution</subject><subject>quadratic convergence</subject><subject>reduction to one-dimensional equations</subject><subject>zeros</subject><issn>0020-7160</issn><issn>1029-0265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1990</creationdate><recordtype>article</recordtype><recordid>eNp1kEFOwzAQRS0EEqVwAHa-QGDsxI4tsUEV0EqVWADraJzYYJTaxU5BuT2p2h1iNaP5783iE3LN4IaBglsADjWTGkApKJWuTsiMAdcFcClOyWyfFxMA5-Qi50-YOF3LGVm-xP7bh3eaxzzYTabR0RBD74PFRO3XDgcfQ6arQHd5zyFNcZiO0_oxbm3a9hgs9eGSnDnss706zjl5e3x4XSyL9fPTanG_LlpWlVXBTVmxSnCLQnDlHBqN3AgFrbVc8Fp1rZFacyFMXaJGY21turZTlZFCSVnOCTv8bVPMOVnXbJPfYBobBs2-iuZPFZNzd3B8cDFt8CemvmsGHPuYXMLQ-tyU_-u_HXVkgQ</recordid><startdate>19900101</startdate><enddate>19900101</enddate><creator>Grapsa, T.N.</creator><creator>Vrahatis, M.N.</creator><creator>Bountis, T.C.</creator><general>Gordon and Breach Science Publishers</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19900101</creationdate><title>Solving systems of nonlinear equations In using a rotating hyperplane in</title><author>Grapsa, T.N. ; Vrahatis, M.N. ; Bountis, T.C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1434-2b341452ea5528ffab9a2b580cee25278dcb699255b73a9abee7bdcd84b658663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1990</creationdate><topic>bisection method</topic><topic>dimension-reducing method</topic><topic>G.1.5</topic><topic>implicit function theorem</topic><topic>imprecise function values</topic><topic>m-step SOR-Newton</topic><topic>Newton's method</topic><topic>nonlinear equations</topic><topic>nonlinear SOR</topic><topic>numerical solution</topic><topic>quadratic convergence</topic><topic>reduction to one-dimensional equations</topic><topic>zeros</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Grapsa, T.N.</creatorcontrib><creatorcontrib>Vrahatis, M.N.</creatorcontrib><creatorcontrib>Bountis, T.C.</creatorcontrib><collection>CrossRef</collection><jtitle>International journal of computer mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Grapsa, T.N.</au><au>Vrahatis, M.N.</au><au>Bountis, T.C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Solving systems of nonlinear equations In using a rotating hyperplane in</atitle><jtitle>International journal of computer mathematics</jtitle><date>1990-01-01</date><risdate>1990</risdate><volume>35</volume><issue>1-4</issue><spage>133</spage><epage>151</epage><pages>133-151</pages><issn>0020-7160</issn><eissn>1029-0265</eissn><abstract>A procedure which accelerates the convergence of iterative methods for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in
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, whose rotation axis depends on the current approximation n-1 of components of the solution. The proposed procedure is applied here on the traditional Newton's method and on a recently proposed "dimension-reducing" method [5] which incorporates the advantages of nonlinear SOR and Newton's algorithms. In this way, two new modified schemes for solving nonlinear systems are correspondingly obtained. For both of these schemes proofs of convergence are given and numerical applications are presented.</abstract><pub>Gordon and Breach Science Publishers</pub><doi>10.1080/00207169008803894</doi><tpages>19</tpages></addata></record> |
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| identifier | ISSN: 0020-7160 |
| ispartof | International journal of computer mathematics, 1990-01, Vol.35 (1-4), p.133-151 |
| issn | 0020-7160 1029-0265 |
| language | eng |
| recordid | cdi_crossref_primary_10_1080_00207169008803894 |
| source | Taylor & Francis |
| subjects | bisection method dimension-reducing method G.1.5 implicit function theorem imprecise function values m-step SOR-Newton Newton's method nonlinear equations nonlinear SOR numerical solution quadratic convergence reduction to one-dimensional equations zeros |
| title | Solving systems of nonlinear equations In using a rotating hyperplane in |
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