, Volume 45, Issue 4, pp 355-367

Recurrence relations for rational cubic methods II: The Chebyshev method

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Abstract

We continue the analysis of rational cubic methods, initiated in [7]. 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.

Zusammenfassung

Wir betrachten ein System von a priori Fehlerabschätzungen für die Konvergenz des Chebyshev-Verfahrens in, Banachräumen. Unsere Sätze geben hinreichende Bedingungen an, den Startwert, welche die Konvergenz der Chebyshev-Iteration sichern. Sie bestehen aus einem System rekursiver Beziehungen, ähnlich den Bedingungen von Kantorvich für das Newton-Verfahren.

This paper is part of the PhD dissertation, realized under the direction, of the second named author.
Supported in part by C.A.I.C.Y.T. GR85-0035. University of Valencia (Spain).