An improved error analysis for the Secant method under the Gamma condition. | [Punjab University Journal of Mathematics • 2007]

Author(s):

1. Ioannis K. Argyros: Cameron University, Department of Mathematical Sciences Lawton, OK, USA

Abstract:

We provide sufficient convergence conditions for the Secant method for approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is a type of gamma condition first introduced in [9] for the study of Newton’s method. Our sufficient convergence condition reduces to the one obtained in [12] for Newton’s method although in general it can be weaker. A numerical example is also provided.

Page(s): 1-11

DOI: DOI not available

Published: Journal: Punjab University Journal of Mathematics, Volume: 39, Issue: 0, Year: 2007

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