An optimal three-point eighth-order iterative method without memory for\n solving nonlinear equations with its dynamics

2016/02/22 by Gunar Matthies, Matthies, Gunar, Mehdi Salimi +4
Mathematics · #Iterative Methods for Nonlinear Equations #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.1602.07026

Abstract

We present a three-point iterative method without memory for solving\nnonlinear equations in one variable. The proposed method provides convergence\norder eight with four function evaluations per iteration. Hence, it possesses a\nvery high computational efficiency and supports Kung and Traub's conjecture.\nThe construction, the convergence analysis, and the numerical implementation of\nthe method will be presented. Using several test problems, the proposed method\nwill be compared with existing methods of convergence order eight concerning\naccuracy and basin of attraction. Furthermore, some measures are used to judge\nmethods with respect to their performance in finding the basin of attraction.\n

Citations

• Optimal Order of One-Point and Multipoint Iteration
• Some fourth order multipoint iterative methods for solving equations

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