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.
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Hernández, M.A. Reduced Recurrence Relations for the Chebyshev Method. Journal of Optimization Theory and Applications 98, 385–397 (1998). https://doi.org/10.1023/A:1022641601991
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DOI: https://doi.org/10.1023/A:1022641601991