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A unified approach for the convergence of certain numerical algorithms, using recurrent functions

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Abstract

The Kantorovich analysis (Argyros in Convergence and applications of Newton-type iterations, Springer, New York, 2008; Argyros and Hilout in Efficient methods for solving equations and variational inequalities, Polimetrica Publisher, Milano, 2009; Kantorovich and Akilov in Functional analysis, Pergamon Press, Oxford, 1982), and recurrent relation’s approach (Gutiérrez et al. in J Comput Appl Math 115:181–192, 2000) are the most popular ways for generating sufficient conditions for the convergence of numerical algorithms to a solution of a nonlinear equations as well as providing the corresponding error estimates on the distances involved. We introduce the new approach of recurrent functions to show that a finer convergence analysis can be provided under the same hypotheses, and computational cost. Numerical examples are provided where our results apply, but not earlier ones.

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Authors and Affiliations

  1. Department of Mathematics Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Laboratoire de Mathématiques et Applications, Poitiers University, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Saïd Hilout

Authors
  1. Ioannis K. Argyros
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  2. Saïd Hilout
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Correspondence to Ioannis K. Argyros.

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Communicated by C.C. Douglas.

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Argyros, I.K., Hilout, S. A unified approach for the convergence of certain numerical algorithms, using recurrent functions. Computing 90, 131–164 (2010). https://doi.org/10.1007/s00607-010-0113-0

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