A note on a modification of Moser's method

  1. Gutiérrez, J.M. 1
  2. Hernández, M.A. 1
  3. Romero, N. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Complexity

ISSN: 0885-064X

Any de publicació: 2008

Volum: 24

Número: 2

Pàgines: 185-197

Tipus: Article

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DOI: 10.1016/J.JCO.2007.04.003 SCOPUS: 2-s2.0-40749130430 WoS: WOS:000255291800008 GOOGLE SCHOLAR

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Resum

We use a recurrence technique to obtain semilocal convergence results for Ulm's iterative method to approximate a solution of a nonlinear equation F (x) = 0fenced((x n + 1 = x n - B n F (x n),, n ≥ 0,; B n + 1 = 2 B n - B n F ′ (x n + 1) B n,, n ≥ 0 .))This method does not contain inverse operators in its expression and we prove it converges with the Newton rate. We also use this method to approximate a solution of integral equations of Fredholm-type. © 2007 Elsevier Inc. All rights reserved.