, Volume 45, Issue 4, pp 355–367

Recurrence relations for rational cubic methods II: The Chebyshev method

  • V. Candela
  • A. Marquina


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.

AMS Subject Classification (1980)

Primary 65J15 

Key words

Third order iterative methods a priori error bounds non-linear equations 

Rekursions-Beziehungen für rationale kubische Verfahren II: Die Chebyshev Methode


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.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • V. Candela
    • 1
  • A. Marquina
    • 1
  1. 1.Departamento de Análisis MatemáticoBurjassot, ValenciaSpain

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