New uni-parametric family of multipoint methods with memory for systems of nonlinear equations

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• 作者：Mona Narang ; Saurabh Bhatia ; Vinay Kanwar
• 关键词：System of nonlinear equations ; R ; order of convergence ; Newton’s method ; Multipoint methods ; Computational efficiency
• 刊名：SeMA Journal
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：74
• 期：1
• 页码：91-113
• 全文大小：
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Milan
• ISSN：2281-7875
• 卷排序：74

文摘

Based on McDougall and Wotherspoon method (Appl Math Lett 29:20–25, 2014) for solving a scalar nonlinear equation, we present a new uni-parametric family of multipoint methods with memory for solving systems of nonlinear equations numerically. The proposed family requires only one Jacobian inversion per iterate and is obtained by using the weight function approach. It is proved that the proposed methods are more efficient than the existing methods, particularly when the size of the nonlinear system is large and high accuracy is required.