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Recurrence relations for rational cubic methods. II: The Chebyshev method. (English) Zbl 0714.65061
Summary: We continue the analysis of rational cubic methods, initiated in part I [ibid. 44, No.2, 169-184 (1990; Zbl 0701.65043)]. In this paper, we obtain a system of a priori error bounds for the Chebyshev method in Banach spaces through a local convergence theorem that provides sufficient conditions on the initial point in order to ensure the convergence of Chebyshev iterates. The error estimates are exact for second degree polynomials. We also discuss some applications.

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