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

  1. Grau-Sánchez, M. 1
  2. Peris, J.M. 1
  3. Gutiérrez, J.M. 2
  1. 1 Universitat Politècnica de Catalunya
    info

    Universitat Politècnica de Catalunya

    Barcelona, España

    GRID grid.6835.8

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Journal:
Applied Mathematics and Computation

ISSN: 0096-3003

Year of publication: 2007

Volume: 190

Issue: 2

Pages: 1815-1823

Type: Article

Export: RIS
DOI: 10.1016/j.amc.2007.02.068 SCOPUS: 2-s2.0-34250672389 WoS: 000248400400087
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Summary

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.