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  • 1
    Digitale Medien
    Digitale Medien
    Reduced Recurrence Relations for the Chebyshev Method (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 385-397 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Chebyshev method ; nonlinear equations in Banach spaces ; third-order methods ; recurrence relations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, we give sufficient conditions ensuring the convergence of the Chebyshev method in Banach spaces. We use a new system of recurrence relations which simplifies those given by Kantorovich for the Newton method or those given by Candela and Marquina for the Chebyshev and Halley methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022641601991
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Second-Derivative-Free Variant of the Chebyshev Method for Nonlinear Equations (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 501-515 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Chebyshev method ; nonlinear equations in Banach spaces ; third-order methods ; multipoint iterations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, we introduce a numerical method for nonlinear equations, based on the Chebyshev third-order method, in which the second-derivative operator is replaced by a finite difference between first derivatives. We prove a semilocal convergence theorem which guarantees local convergence with R-order three under conditions similar to those of the Newton-Kantorovich theorem, assuming the Lipschitz continuity of the second derivative. In a subsequent theorem, the latter condition is replaced by the weaker assumption of Lipschitz continuity of the first derivative.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004618223538
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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