On an efficient -step iterative method for nonlinear equations

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• 作者：S. Amat^a ; ^{sergio.amat@upct.es" class="auth_mail" title="E-mail the corresponding author} ; C. Bermú ; dez^a ; ^{concepcion.bermudez@upct.es" class="auth_mail" title="E-mail the corresponding author} ; M.A. Herná ; ndez-Veró ; n^b ; ^{mahernan@unirioja.es" class="auth_mail" title="E-mail the corresponding author} ; Eulalia Martí ; nez^c ; ^{eumarti@mat.upv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：47H99 ; 65H10
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：258-271
• 全文大小：1177 K

文摘

This paper is devoted to the construction and analysis of an efficient 377042716300437&_mathId=si5.gif&_user=111111111&_pii=S0377042716300437&_rdoc=1&_issn=03770427&md5=7d70da5c4b9b6fa52ff08a2fa437d75b" title="Click to view the MathML source">k$k$-step iterative method for nonlinear equations. The main advantage of this method is that it does not need to evaluate any high order Fréchet derivative. Moreover, all the 377042716300437&_mathId=si5.gif&_user=111111111&_pii=S0377042716300437&_rdoc=1&_issn=03770427&md5=7d70da5c4b9b6fa52ff08a2fa437d75b" title="Click to view the MathML source">k$k$-step have the same matrix, in particular only one LU decomposition is required in each iteration. We study the convergence order, the efficiency and the dynamics in order to motivate the proposed family. We prove, using some recurrence relations, a semilocal convergence result in Banach spaces. Finally, a numerical application related to nonlinear conservative systems is presented.