On Schroder's families of root-finding methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Petkovic, M. S.¹  Petkovic, L. D.²  Herceg, D.³ 

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

[2] Univ Nis, Fac Mech Engn, Nish 18000, Serbia

[3] Univ Novi Sad, Dept Math, Novi Sad 21000, Serbia

关键词: Solving nonlinear equations;    Iteration methods;    Schroder's methods;    Convergence rate;    Priority;    Historical notes;   

DOI  :  10.1016/j.cam.2009.09.012

来源: Elsevier

【 摘 要 】

Schroder's methods of the first and second kind for solving a nonlinear equatior f (x) = 0, originally derived in 1870, are of great importance in the theory and practice of iteration processes. They were rediscovered several times and expressed in different forms during the last 130 years. It was proved in the paper of Petkovic and Herceg (1999) [7] that even seven families of iteration methods for solving nonlinear equations are mutually equivalent. In this paper we show that these families are also equivalent to another four families of iteration methods and find that all of them have the origin in Schroder's generalized method (of the second kind) presented in 1870. In the continuation we consider Smale's open problem from 1994 about possible link between Schroder's methods of the first and second kind and state the link in a simple way. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free