The Ulm method under mild differentiability conditions |
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Authors: | J. A. Ezquerro M. A. Hernández |
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Affiliation: | 1. Department of Mathematics and Computation, University of La Rioja, C/Luis de Ulloa s/n, 26004, Logro?o, Spain
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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 p ω(z), for z > 0, tϵ[0,1] and pϵ[0,1]. Preparation of this paper was partly supported by the Ministry of Education and Science (MTM 2005-03091). |
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Keywords: | 45G10 47H17 65J15 |
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