A semilocal convergence result for Newton's method under generalized conditions of Kantorovich

  1. Ezquerro, J.A. 1
  2. González, D. 1
  3. Hernández-Verón, M.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Complexity

ISSN: 0885-064X

Year of publication: 2014

Volume: 30

Issue: 3

Pages: 309-324

Type: Article

DOI: 10.1016/J.JCO.2013.12.006 SCOPUS: 2-s2.0-84897429134 WoS: WOS:000337642600004 GOOGLE SCHOLAR

More publications in: Journal of Complexity

Abstract

From Kantorovich's theory we establish a general semilocal convergence result for Newton's method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton's method and improve the a priori error estimates. Finally, we illustrate our study with an application to a special case of conservative problems. © 2013 Elsevier Inc. All rights reserved.