Local Convergence of Traub’s Method and Its Extensions

Fractal and Fractional

article

Muhammed Saeed K¹  Krishnendu Remesh¹  Santhosh George¹  Jidesh Padikkal¹  Ioannis K. Argyros² 

[1] Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka;Department of Computing and Mathematical Sciences, Cameron University

关键词: iterative methods;    Arithmetic-Mean Newton’s method;    Weerakoon-Fernando method;    order of convergence;    Taylor series expansion;    Fréchet derivative;   

DOI  :  10.3390/fractalfract7010098

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

In this article, we examine the local convergence analysis of an extension of Newton’s method in a Banach space setting. Traub introduced the method (also known as the Arithmetic-Mean Newton’s Method and Weerakoon and Fernando method) with an order of convergence of three. All the previous works either used higher-order Taylor series expansion or could not derive the desired order of convergence. We studied the local convergence of Traub’s method and two of its modifications and obtained the convergence order for these methods without using Taylor series expansion. The radii of convergence, basins of attraction, comparison of iterations of similar iterative methods, approximate computational order of convergence (ACOC), and a representation of the number of iterations are provided.

【 授权许可】

CC BY