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Title

DYNAMICAL CONTROL OF COMPUTATIONS USING THE FAMILY OF OPTIMAL TWO-POINT METHODS TO SOLVE NONLINEAR EQUATIONS

Pages

 Start Page 139 | End Page 147

Abstract

 One of the considerable discussions for solving the NONLINEAR EQUATIONS is to nd the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal TWO-POINT METHODS, we propose a new scheme based on the STOCHASTIC ARITHMETIC to find the optimal number of iterations in the given iterative solution and obtain the optimal solution with its accuracy. For this purpose, a theorem is proved to illustrate the accuracy of the iterative method and the CESTAC1 method and CADNA2 library are applied which allows us to estimate the round-o error effect on any computed result.The classical criterion to terminate the iterative procedure is replaced by a criterion independent of the given accuracy (e) such that the best solution is evaluated numerically, which is able to stop the process as soon as a satisfactory informatical solution is obtained. Some numerical examples are given to validate the results and show the efficiency and importance of using the STOCHASTIC ARITHMETIC in place of the floating-point arithmetic.

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