Accelerating the convergence of Newton-type iterations-Reference-Cited by-同舟云学术

Accelerating the convergence of Newton-type iterations

Published:2017-10-13 Issue:2 Volume:46 Page:162-180
ISSN:2501-059X
Container-title:Journal of Numerical Analysis and Approximation Theory
language:
Short-container-title:J. Numer. Anal. Approx. Theory

Author:

Zhanlav Tugal,Chuluunbaatar Ochbadrakh,Ulziibayar Vandandoo

Abstract

In this paper, we present a new accelerating procedure in order to speed up the convergence of Newton-type methods. In particular, we derive iterations with a high and optimal order of convergence. This technique can be applied to any iteration with a low order of convergence. As expected, the convergence of the proposed methods was remarkably fast. The effectiveness of this technique is illustrated by numerical experiments.

Publisher

Academia Romana Filiala Cluj

Reference20 articles.

1. W. Bi, H. Ren, Q. Wu, Three-step iterative methods with eighth-order convergence for solving nonlinear equations, J. Comput. Appl. Math., 225 (2009), pp. 105-112, https://doi.org/10.1016/j.cam.2008.07.004

2. A. Cordero, J.L. Hueso, E. Martinez, J. R. Torregrosa, New modifications of Potra-Ptak’s method with optimal fourth and eighth orders of convergence, J. Comput. Appl. Math., 234 (2010), pp. 2969-2976.

3. A. Cordero, J.R. Torregrosa, M.P. Vassileva, Three-step iterative methods with optimal eighthorder convergence, J. Comput. Appl. Math., 235 (2011), pp. 3189-3194, https://doi.org/10.1016/j.cam.2010.04.009

4. J.A. Ezquerro, M.A. Hernandez, N. Romero, A.I. Velasco, Improving the domain of starting points for secant-like methods, Appl. Math. Comput., 219 (2012), pp. 3677-3692, https://doi.org/10.1016/j.amc.2012.09.070

5. L. Fang, G. He, Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations, J. Comput. Appl. Math., 228 (2009), pp. 296-303, https://doi.org/10.1016/j.cam.2008.09.023