Approximation of inverse operators by a new family of high-order iterative methods

  1. Amat, S. 1
  2. Ezquerro, J.A. 2
  3. Hernández-Verón, M.A. 2
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Numerical Linear Algebra with Applications

ISSN: 1070-5325

Year of publication: 2014

Volume: 21

Issue: 5

Pages: 629-644

Type: Article

DOI: 10.1002/NLA.1917 SCOPUS: 2-s2.0-84908310038 WoS: WOS:000343009000004 GOOGLE SCHOLAR

More publications in: Numerical Linear Algebra with Applications

Abstract

SUMMARY: The main goal of this paper is to approximate inverse operators by high-order Newton-type methods with the important feature of not using inverse operators. We analyse the semilocal convergence, the speed of convergence, and the efficiency of these methods. We determine that Chebyshev's method is the most efficient method and test it on two problems: one associated to the heat equation and the other one to a boundary value problem. We consider examples with matrices that are close to be singular and/or are badly conditioned. We check the robustness and the stability of the methods by considering situations with many steps and noised data. © 2013 John Wiley & Sons, Ltd.