On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions
- Hernández-Verón, M.A. 1
- Martínez, E. 2
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1
Universidad de La Rioja
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2
Universidad Politécnica de Valencia
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ISSN: 1017-1398
Argitalpen urtea: 2015
Alea: 70
Zenbakia: 2
Orrialdeak: 377-392
Mota: Artikulua
Beste argitalpen batzuk: Numerical Algorithms
Lotura duten proiektuak
Laburpena
In this paper the semilocal convergence for an alternative to the three steps Newton’s method with frozen derivative is presented. We analyze the generalization of convergence conditions given by w-conditioned non-decreasing functions instead of the first derivative Lipschitz or Holder continuous given by other authors. A nonlinear integral equation of mixed Hammerstein type is considered for illustrating the new theoretical results obtained in this paper, where previous results can not be satisfied.