Accelerated iterative methods for finding solutions of a system of nonlinear equations

  • Grau-Sánchez M
  • Peris J
  • Gutiérrez J
  • 2

    Readers

    Mendeley users who have this article in their library.
  • 19

    Citations

    Citations of this article.

Abstract

In this paper, we present a technique to construct iterative methods to approximate the zeros of a nonlinear equation F (x) = 0, where F is a function of several variables. This technique is based on the approximation of the inverse function of F and on the use of a fixed point iteration. Depending on the number of steps considered in the fixed point iteration, or in other words, the number of evaluations of the function F, we obtain some variants of classical iterative processes to solve nonlinear equations. These variants improve the order of convergence of classical methods. Finally, we show some numerical examples, where we use adaptive multi-precision arithmetic in the computation that show a smaller cost. © 2007 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Iterative methods
  • Newton's method
  • Nonlinear equations
  • Order of convergence
  • Zero of a function

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Miquel Grau-Sánchez

  • Josep M. Peris

  • José M. Gutiérrez

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free