Zero-finder methods derived from Obreshkov’s techniques |
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Authors: | Miquel Grau-Sánchez José M Gutiérrez |
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Institution: | a Technical University of Catalonia, Department of Applied Mathematics II, Jordi Girona 1-3, Omega, 08034 Barcelona, Spain b University of La Rioja, Department of Mathematics and Computation, Luis Ulloa s/n, 26004 Logroño, Spain |
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Abstract: | In this paper two families of zero-finding iterative methods for solving nonlinear equations f(x)=0 are presented. The key idea to derive them is to solve an initial value problem applying Obreshkov-like techniques. More explicitly, Obreshkov’s methods have been used to numerically solve an initial value problem that involves the inverse of the function f that defines the equation. Carrying out this procedure, several methods with different orders of local convergence have been obtained. An analysis of the efficiency of these methods is given. Finally we introduce the concept of extrapolated computational order of convergence with the aim of numerically test the given methods. A procedure for the implementation of an iterative method with an adaptive multi-precision arithmetic is also presented. |
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Keywords: | Obreshkov&rsquo s methods Nonlinear equations Iterative methods Order of convergence Efficiency |
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