On generalized biparametric multipoint root finding methods with memory

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:255

Article

Dzunic, Jovana¹  Petkovic, Miodrag S.¹ 

[1] Univ Nis, Dept Math, Fac Elect Engn, Nish 18000, Serbia

关键词: Nonlinear equations;    Root-finders;    Multipoint methods;    Convergence acceleration;    Computational efficiency;   

DOI  :  10.1016/j.cam.2013.05.013

来源: Elsevier

【 摘 要 】

A general family of biparametric n-point methods with memory for solving nonlinear equations is proposed using an original accelerating procedure with two parameters. This family is based on derivative free classes of n-point methods without memory of interpolatory type and Steffensen-like method with two free parameters. The convergence rate of the presented family is considerably increased by self-accelerating parameters which are calculated in each iteration using information from the current and previous iteration and Newton's interpolating polynomials with divided differences. The improvement of convergence order is achieved without any additional function evaluations so that the proposed family has a high computational efficiency. Numerical examples are included to confirm theoretical results and demonstrate convergence behavior of the proposed methods. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free