Majorizing functions and two-point Newton-type methods

Authors:
Jinhai Chen;Ioannis K. Argyros;Ravi P. Agarwal
Affiliations:
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Campus Box 170, P.O. Box 173364, Denver, CO 80217-3364, USA;Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA;Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The semi-local convergence of a Newton-type method used to solve nonlinear equations in a Banach space is studied. We also give, as two important applications, convergence analyses of two classes of two-point Newton-type methods including a method mentioned in [5] and the midpoint method studied in [1,2,12]. Recently, interest has been shown in such methods [3,4].