Analysing the efficiency of some modifications of the secant method

Authors:
J. A. Ezquerro;A. Grau;M. Grau-SáNchez;M. A. HernáNdez;M. Noguera
Affiliations:
Department of Mathematics and Computation, University of La Rioja, E-26004 Logroño, Spain;Department of Applied Mathematics II, Technical University of Catalonia, E-08034 Barcelona, Spain;Department of Applied Mathematics II, Technical University of Catalonia, E-08034 Barcelona, Spain;Department of Mathematics and Computation, University of La Rioja, E-26004 Logroño, Spain;Department of Applied Mathematics II, Technical University of Catalonia, E-08034 Barcelona, Spain
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

Some modifications of the secant method for solving nonlinear equations are revisited and the local order of convergence is found in a direct symbolic computation. To do this, a development of the inverse of the first order divided differences of a function of several variables in two points is presented. A generalisation of the efficiency index used in the scalar case to several variables is also analysed in order to use the most competitive algorithm.