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The Ulm method under mild differentiability conditions

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Abstract

The Ulm method is considered to approximate a solution of a nonlinear operator equation F(x) = 0. We study the convergence of this method when F′ is ω-conditioned and prove that the R-order of convergence is at least 1 + p if ω is quasi-homogeneous of type ω(tz)≤ t pω(z), for z > 0, tϵ[0,1] and pϵ[0,1].

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Authors and Affiliations

  1. Department of Mathematics and Computation, University of La Rioja, C/Luis de Ulloa s/n, 26004, Logroño, Spain

    J. A. Ezquerro & M. A. Hernández

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  1. J. A. Ezquerro
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  2. M. A. Hernández
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Correspondence to J. A. Ezquerro.

Additional information

Preparation of this paper was partly supported by the Ministry of Education and Science (MTM 2005-03091).

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Ezquerro, J.A., Hernández, M.A. The Ulm method under mild differentiability conditions. Numer. Math. 109, 193–207 (2008). https://doi.org/10.1007/s00211-008-0144-z

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  • DOI: https://doi.org/10.1007/s00211-008-0144-z

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