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Recurrence relations for rational cubic methods. I: The Halley method. (English) Zbl 0701.65043
Authors’ summary: 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 B. Döring [Apl. Mat. 15, 418-464 (1970; MR 44.1210)]. The error bounds presented are optimal for second degree polynomials. Other rational cubic method, as the Chebyshev method, will be treated in a subsequent paper.
Reviewer: J.Kolomý

MSC:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
References:
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