Exact order of convergence of the secant method |
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Authors: | M Raydan |
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Institution: | (1) Escuela de Computacion, Universidad Central de Venezuela, Caracas, Venezuela |
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Abstract: | We study the exact order of convergence of the secant method when applied to the problem of finding a zero of a nonlinear function defined from into . Under the standard assumptions for which Newton's method has the exact Q-order of convergencep, wherep is some positive integer, we establish that the secant method has the Q-order and the exact R-order of convergence
. We prove also that, forp=2 andp=3, the secant method has the exact Q-order of convergenceS(p). Moreover, we present a counterexample to show that, forp 4, it may not have an exact Q-order of convergence.The author wishes to thank Florian Potra, Richard Tapia, and the referees for helpful comments and suggestions.This paper was prepared while the author was Visiting Professor, Department of Mathematics, University of Kentucky, Lexington, Kentucky. |
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Keywords: | Order of convergence Newton's method secant method |
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