A SIMPLE AND EFFICIENT ROOT-FINDING ALGORITHM FOR DEALING WITH SCALAR NONLINEAR EQUATIONS: ITERATIVE PROCEDURE BASED ON GEOMETRIC CONSIDERATIONS

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Published: 2018-12-06

Page: 388-412


GREGORY ANTONI *

Aix-Marseille Universite, IFSTTAR, LBA UMR T24, F-13016 Marseille, France

*Author to whom correspondence should be addressed.


Abstract

In this study, we present a simple and efficient root-finding algorithm for approximating the solution of scalar nonlinear equations. The proposed iterative scheme is based on geometric considerations using only the first-order derivative associated with the nonlinear function in question. The predictive capabilities of this numerical procedure for providing an accurate approximate solution associated with a nonlinear equation are tested, assessed and discussed on some examples.

Keywords: Scalar nonlinear equations, root-finding iterative algorithm, Newton’s algorithm, substeps iterative scheme, geometric approach


How to Cite

ANTONI, G. (2018). A SIMPLE AND EFFICIENT ROOT-FINDING ALGORITHM FOR DEALING WITH SCALAR NONLINEAR EQUATIONS: ITERATIVE PROCEDURE BASED ON GEOMETRIC CONSIDERATIONS. Asian Journal of Mathematics and Computer Research, 25(7), 388–412. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/4342

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