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IMA Journal of Numerical Analysis 1997 17(4):511-525; doi:10.1093/imanum/17.4.511
© 1997 by Institute of Mathematics and its Applications
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A modification of the Chebyshev method

JOSÉ A. EZQUERRO

University of La Rioja, Department of Mathematics and Computacion C/Luis de Ulloa s/n, 26004, Logrono, Spain

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 {alpha} ≥ 0.


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