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

Revue:
Numerical Linear Algebra with Applications

ISSN: 1070-5325

Année de publication: 2014

Volumen: 21

Número: 5

Pages: 629-644

Type: Article

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

D'autres publications dans: Numerical Linear Algebra with Applications

Dépôt institutionnel: lockAccès ouvert Editor

Projets liés

Procesos iteratios para resolver ecuaciones no lineales: construcción, convergencia, eficacia, análisis dinámico y aplicaciones

2012/00014/001

Résumé

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.