New efficient methods for solving nonlinear systems of equations with arbitrary even order

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• 作者：Saeid Abbasbandy^a ; ^{abbasbandy@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Parisa Bakhtiari^d ; ^{bakhtiaripr@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Alicia Cordero ; ^c ; ^{acordero@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Juan R. Torregrosa^c ; ^{jrtorre@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Taher Lotfi^b ; ^{lotfitaher@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlinear systems ; Multipoint iteration ; Matrix LU factorization ; Computational efficiency
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 September 2016
• 年：2016
• 卷：287-288
• 期：Complete
• 页码：94-103
• 全文大小：378 K

文摘

In 2011, Khattri and Abbasbandy developed an optimal two-step Jarratt-like method for approximating simple roots of a nonlinear equation. We develop their method for solving nonlinear systems of equations. The main feature of the extended methods is that it uses only one LU factorization which preserves and reduces computational complexities. Following this aim, the suggested method is generalized in such a way that we increase the order of convergence but we do not need new LU factorization. Convergence and complexity analysis are provided rigorously. Using some small and large systems, applicability along with some comparisons are illustrated.