Improving order and efficiency: Composition with a modified Newton's method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:231

Article

Grau-Sanchez, Miquel

关键词: Newton method;    Nonlinear equations;    Iterative methods;    Order of convergence;    Efficiency;   

DOI  :  10.1016/j.cam.2009.04.002

来源: Elsevier

【 摘 要 】

In this paper a zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton's method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain new methods that can be generalized in Banach spaces. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free