Improved Algorithms Of Illinois-Type For The Numerical Solution Of Nonlinear Equations
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author = {J. A. Ford},
title = {Improved Algorithms Of Illinois-Type For The Numerical Solution Of Nonlinear Equations},
year = {}
}
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Abstract:
An approach is described for the construction of a class of derivative-free methods for the solution of a single nonlinear equation in one variable and several new methods are obtained. The prototype for the class is the so-called "Illinois" Method (Dowell and Jarratt [1]), which itself is a variant of the classical method of Regula Falsi. These methods deal with the problem of "end-point retention" in Regula Falsi and the consequent failure to achieve superlinear convergence by modifying (with a suitably-chosen scaling factor) one of the function-values used in the linear interpolation. The results of numerical experiments on new and existing algorithms in the class are reported, indicating that the performance of some of the new methods obtained here is very promising. The local convergence of these methods is analysed and the asymptotic orders of convergence and patterns of behaviour are determined and compared with those of existing methods. e-mail: fordj@essex.ac.uk 1 INTRODUC...
Citations
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