Journal Article

A modification of the Chebyshev method

JOSÉ A. EZQUERRO

in IMA Journal of Numerical Analysis

Published on behalf of Institute of Mathematics and its Applications

Volume 17, issue 4, pages 511-525
Published in print October 1997 | ISSN: 0272-4979
Published online October 1997 | e-ISSN: 1464-3642 | DOI: https://dx.doi.org/10.1093/imanum/17.4.511
A modification of the Chebyshev method

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In this paper we use a one-parametric family of second-order iterations to solve a nonlinear operator equation in a Banach space. Two different analyses of convergence are shown. First, under standard Newton-Kantorovich conditions, we establish a Kantorovich-type convergence theorem. Second, another Kantorovich-type convergence theorem is proved, when the first Fréchet-derivative of the operator satisfies a Lipschitz condition. We also give an explicit expression for the error bound of the family of methods in terms of a real parameter α ≥ 0.

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Subjects: Mathematics

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