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

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FARIBORZI ARAGHI M.A.; ZAREI E.

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Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2017 | Volume:9 | Issue:2 Page(s): 139-147

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Title

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

Author(s)

FARIBORZI ARAGHI M.A. | ZAREI E. | Issue Writer Certificate

Keywords

STOCHASTIC ARITHMETICQ2

CESTAC METHODQ2

CADNA LIBRARYQ2

TWO-POINT METHODSQ2

NONLINEAR EQUATIONSQ2

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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APA: Copy

FARIBORZI ARAGHI, M.A., & ZAREI, E.. (2017). DYNAMICAL CONTROL OF COMPUTATIONS USING THE FAMILY OF OPTIMAL TWO-POINT METHODS TO SOLVE NONLINEAR EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 9(2), 139-147. SID. https://sid.ir/paper/231798/en

Vancouver: Copy

FARIBORZI ARAGHI M.A., ZAREI E.. DYNAMICAL CONTROL OF COMPUTATIONS USING THE FAMILY OF OPTIMAL TWO-POINT METHODS TO SOLVE NONLINEAR EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2017;9(2):139-147. Available from: https://sid.ir/paper/231798/en

IEEE: Copy

M.A. FARIBORZI ARAGHI, and E. ZAREI, “DYNAMICAL CONTROL OF COMPUTATIONS USING THE FAMILY OF OPTIMAL TWO-POINT METHODS TO SOLVE NONLINEAR EQUATIONS,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 9, no. 2, pp. 139–147, 2017, [Online]. Available: https://sid.ir/paper/231798/en

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