On a two-step relaxed Newton-type method

  1. Amat, S. 12
  2. Magreñán, Á.A. 12
  3. Romero, N. 12
  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:
Applied Mathematics and Computation

ISSN: 0096-3003

Year of publication: 2013

Volume: 219

Issue: 24

Pages: 11341-11347

Type: Article

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DOI: 10.1016/J.AMC.2013.04.061 SCOPUS: 2-s2.0-84879613198 WoS: WOS:000322502900024 GOOGLE SCHOLAR

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Abstract

We propose a new two-step relaxed Newton-type method for the approximation of nonlinear equations in Banach spaces. The method is free of any bilinear operator. Moreover, in each iteration, we only approximate an associated linear system. We analyze its semilocal convergence under ω-conditioned divided differences. Finally, we include several practical advantages of the method. © 2013 Elsevier Inc. All rights reserved.