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Recurrence Relations for Chebyshev-Type Methods

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Abstract.

The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A , instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the methods introduced here accelerate the classical Newton iteration for a suitable A is provided.

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Authors and Affiliations

  1. Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, 26004 Logrono, Spain, jezquer@dmc.unirioja.es, mahernan@dmc.unirioja.es, , , , , , ES

    J. A. Ezquerro & M. A. Hernández

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  1. J. A. Ezquerro
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  2. M. A. Hernández
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Accepted 23 October 1998

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Ezquerro, J., Hernández, M. Recurrence Relations for Chebyshev-Type Methods . Appl Math Optim 41, 227–236 (2000). https://doi.org/10.1007/s002459911012

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  • DOI: https://doi.org/10.1007/s002459911012

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