An optimal class of eighth-order iterative methods based on Kung and Traub's method with its dynamics

2015/08/07 by Gunar Matthies, Matthies, Gunar, Mehdi Salimi +4
Computer Science · Mathematics · #37F10 #65H05 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1508.01748

openalex publication_date 2015/08/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a three-point without memory iterative method based on Kung and Traub's method for solving non-linear equations in one variable. The proposed method has eighth-order convergence and costs only four function evaluations each iteration which supports the Kung-Traub conjecture on the optimal order of convergence. Consequently, this method possesses very high computational efficiency. We present the construction, the convergence analysis, and the numerical implementation of the method. Furthermore, comparisons with some other existing optimal eighth-order methods concerning accuracy and basins of attraction for several test problems will be given.

Citations

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

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