Recurrence relations for rational cubic methods I: The Halley method |
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Authors: | V Candela A Marquina |
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Affiliation: | 1. Departmento de Análisis Matemático, University of Valencia, C/Dr. Moliner, 50, 46100, Burjassot (Valencia), Spain
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Abstract: | In this paper we present a system of a priori error bounds for the Halley method in Banach spaces. Our theorem supplies sufficient conditions on the initial point to ensure the convergence of Halley iterates, by means of a system of “recurrence relations”, analogous to those given for the Newton method by Kantorovich, improving previous results by Döring 4]. The error bounds presented are optimal for second degree polynomials. Other rational cubic methods, as the Chebyshev method, will be treated in a subsequent paper. |
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