Document Zbl 1535.65065

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Algorithms</a> <a href="/?q=in%3A510294" title="Articles in this Issue">95, No. 4, 1879-1904 (2024)</a>. </div> <div class="abstract">Summary: In this manuscript, we present a new class of highly efficient two-parameter optimal iterative methods for solving nonlinear systems that generalizes Ostrowski’s method, King’s Family, Chun’s method, and KLAM Family in multidimensional context. This class is an extension to systems of the Ermakov’s Hyperfamily. The fourth order of convergence of the members of the class is demonstrated, thus obtaining optimal schemes for solving nonlinear systems. The high efficiency of the elements of the class is studied, compared with other known methods of the same order or even higher, and some numerical proofs are presented. We also analyze its robustness.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7824753">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65H10" title="MSC2020">65H10</a> </td> <td class="space"> Numerical computation of solutions to systems of equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65H05" title="MSC2020">65H05</a> </td> <td class="space"> Numerical computation of solutions to single equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anonlinear+systems">nonlinear systems</a>; <a href="/?q=ut%3Aiterative+methods">iterative methods</a>; <a href="/?q=ut%3AErmakov%27s+hyperfamily">Ermakov’s hyperfamily</a>; <a href="/?q=ut%3Adynamical+analysis">dynamical analysis</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Aorder+of+convergence">order of convergence</a>; <a href="/?q=ut%3Aoptimal+method+for+systems">optimal method for systems</a>; <a href="/?q=ut%3Ahighly+efficient+methods">highly efficient methods</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1535.65065" data-ciurl="/ci/07824753" data-biburl="/bibtex/07824753.bib" data-amsurl="/amsrefs/07824753.bib" data-xmlurl="/xml/07824753.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07824753.pdf" title="Zbl 1535.65065 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s11075-023-01631-9" aria-label="DOI for “A highly efficient class of optimal fourth-order methods for solving nonlinear systems”" title="10.1007/s11075-023-01631-9">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Sharma, JR; Kumar, S., A class of accurate Newton-Jarratt-like methods with applications to nonlinear models, Computational and Applied Mathematics, 41, 1, 46, 2022 · <a href="/1499.65191" class="nowrap">Zbl 1499.65191</a> · <a href="https://doi.org/10.1007/s40314-021-01739-5" class="nowrap">doi:10.1007/s40314-021-01739-5</a></td> </tr><tr> <td>[2]</td> <td class="space">Behl, R.; Bhalla, S.; Magreñán, ÁA; Kumar, S., An efficient high order iterative scheme for large nonlinear systems with dynamics, Journal of Computational and Applied Mathematics, 404, 2022 · <a href="/1481.65075" class="nowrap">Zbl 1481.65075</a> · <a href="https://doi.org/10.1016/j.cam.2020.113249" class="nowrap">doi:10.1016/j.cam.2020.113249</a></td> </tr><tr> <td>[3]</td> <td class="space">Solaiman, OS; Hashim, I., An iterative scheme of arbitrary odd order and its basins of attraction for nonlinear systems, Comput. 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Lett., 25, 2369-2374, 2012 · <a href="/1252.65093" class="nowrap">Zbl 1252.65093</a> · <a href="https://doi.org/10.1016/j.aml.2012.07.005" class="nowrap">doi:10.1016/j.aml.2012.07.005</a></td> </tr><tr> <td>[20]</td> <td class="space">Cordero, A.; Hueso, JL; Torregrosa, JR, Variants of Newton’s method using fifth-order quadrature formulas, Applied Mathematics and Computation, 190, 686-698, 2012 · <a href="/1122.65350" class="nowrap">Zbl 1122.65350</a> · <a href="https://doi.org/10.1016/j.amc.2007.01.062" class="nowrap">doi:10.1016/j.amc.2007.01.062</a></td> </tr><tr> <td>[21]</td> <td class="space">Grau-Sánchez, M.; Noguera, M.; Gutiérrez, J., On some computational orders of convergence, Applied Mathematics Letters, 23, 472-478, 2010 · <a href="/1189.65092" class="nowrap">Zbl 1189.65092</a> · <a href="https://doi.org/10.1016/j.aml.2009.12.006" class="nowrap">doi:10.1016/j.aml.2009.12.006</a></td> </tr><tr> <td>[22]</td> <td class="space">Grau-Sánchez, M.; Noguera, M.; Gutiérrez, J., On new computational local orders of convergence, Applied Mathematics Letters, 25, 2023-2030, 2012 · <a href="/1252.65091" class="nowrap">Zbl 1252.65091</a> · <a href="https://doi.org/10.1016/j.aml.2012.04.012" class="nowrap">doi:10.1016/j.aml.2012.04.012</a></td> </tr><tr> <td>[23]</td> <td class="space">Burden, R.L., Faires, J.D.: Numerical analysis. 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