On the local and semilocal convergence of a parameterized multi-step Newton method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:376

Article

Amat, S.¹  Argyros, I²  Busquier, S.¹  Hernandez-Veron, M. A.³  Yanez, D. F.⁴ 

[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain

[2] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[3] Univ La Rioja, Dept Matemat & Comp, Logrono, Spain

[4] Univ Valencia, Dept Matemat, Valencia, Spain

关键词: Iterative processes;    Multi-step Newton's method;    Local convergence;    Semilocal convergence;   

DOI  :  10.1016/j.cam.2020.112843

来源: Elsevier

【 摘 要 】

This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-step iterative methods are computationally attractive. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free