A NEW ITERATIVE ALGORITHM FOR APPROXIMATING ZEROS OF NONLINEAR SCALAR EQUATIONS: GEOMETRY-BASED SOLVING PROCEDURE

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Published: 2015-12-04

Page: 78-97


GREGORY ANTONI *

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

*Author to whom correspondence should be addressed.


Abstract

This paper is devoted to a new iterative method for solving nonlinear scalar equations. Based on some geometric considerations, the proposed numerical procedure takes into account the local curvature of the studied function. Indeed, the accuracy of the approximate solution provides by the standard Newton's method can be improved, in some cases, depending on the inherent nonlinearity of the function in question. This new iterative method is tested and assessed on some examples.

Keywords: Nonlinear scalar equations, Iterative algorithms;, Newton's method, Frenet formulas, Geometric approach


How to Cite

ANTONI, G. (2015). A NEW ITERATIVE ALGORITHM FOR APPROXIMATING ZEROS OF NONLINEAR SCALAR EQUATIONS: GEOMETRY-BASED SOLVING PROCEDURE. Asian Journal of Mathematics and Computer Research, 10(2), 78–97. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/249

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