A GEOMETRY-BASED ITERATIVE ALGORITHM FOR FINDING THE APPROXIMATE SOLUTIONS OF SYSTEMS OF NONLINEAR EQUATIONS

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Published: 2018-12-06

Page: 413-431


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 finding the approximate solutions of systems of nonlinear equations. Based on some geometric considerations, a root-finding algorithm applied to a single equation is developed and coupled with Jacobi and Gauss-Seidel procedures with the aim of solving nonlinear systems. The numerical predictive abilities of this iterative method are addressed and discussed on some examples.

Keywords: Systems of nonlinear equations, iterative algorithms, newton’s method, Gauss-Seidel’s procedure, Jacobi’s procedure


How to Cite

ANTONI, G. (2018). A GEOMETRY-BASED ITERATIVE ALGORITHM FOR FINDING THE APPROXIMATE SOLUTIONS OF SYSTEMS OF NONLINEAR EQUATIONS. Asian Journal of Mathematics and Computer Research, 25(7), 413–431. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/4343

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