On a family of high-order iterative methods under gamma conditions with applications in denoising

  1. Amat, S. 1
  2. Hernández, M.A. 2
  3. Romero, N. 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:
Numerische Mathematik

ISSN: 0029-599X

Year of publication: 2014

Volume: 127

Issue: 2

Pages: 201-221

Type: Article

DOI: 10.1007/S00211-013-0589-6 SCOPUS: 2-s2.0-84901244221 WoS: WOS:000336027000001 GOOGLE SCHOLAR

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Abstract

We study a class of at least third order iterative methods for nonlinear equations on Banach spaces. A characterization of the convergence under Gamma-type conditions is presented. Though, in general, these methods are not very extended due to their computational costs, we can find examples in which they are competitive and even cheaper than other simpler methods. Indeed, we propose a new nonlinear mathematical model for the denoising of digital images, where the best method in the family has fourth order of convergence. Moreover, our family includes two-step Newton type methods with good numerical behavior in general. We center our analysis in both, analytic and computational, aspects. © 2013 Springer-Verlag Berlin Heidelberg.