Secant-type methods and nondiscrete induction

Authors:
Ioannis K. Argyros;Saïd Hilout
Affiliations:
Department of Mathematics Sciences, Cameron University, Lawton, USA 73505;Laboratoire de Mathématiques et Applications, Poitiers University, Futuroscope Chasseneuil Cedex, France 86962
Venue:
Numerical Algorithms
Year:
2012

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Abstract

The celebrated nondiscrete mathematical induction has been used to improve error bounds of distances involved in the discrete case but not the sufficient convergence conditions for Secant---type methods. We show that using the same information as before, the following advantages can be obtained: weaker sufficient convergence conditions; tighter error bounds on the distances involved and a more precise information on the location of the solution. Numerical examples validating the theoretical conclusions are also provided in this study.