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A Note on a Family of Newton Type Iterative Processes

Summary: A Note on a Family of Newton Type
Iterative Processes
J.A. Ezquerro and M.A. Hern´andez
University of La Rioja, Department of Mathematics and Computation
C/ Luis de Ulloa s/n, 26004, Logro~no, Spain
In this paper, we study the convergence of a family of iteration
methods to solve nonlinear equations in the complex plane. Two
analysis of convergence are provided. We give a Kantorovich-type
convergence theorem under mild differentiability conditions with er-
ror analysis.
Keywords: Nonlinear equations in complex plane, second-order
processes, Newton method, Newton-Kantorovich assumptions, majorizing
Classification A.M.S. 1991: 26A51, 65H05.
Supported in part by a grant of the University of La Rioja.
1 Introduction
Hern´andez and Salanova [5] define a new family of iterative processes of
second order depending on a real parameter 0 by
x,n+1 = x,n -


Source: Amat, Sergio - Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena


Collections: Mathematics