A GEOMETRY-BASED ITERATIVE ALGORITHM FOR FINDING THE APPROXIMATE SOLUTIONS OF SYSTEMS OF NONLINEAR EQUATIONS
GREGORY ANTONI *
Aix-Marseille Universite, IFSTTAR, LBA UMR T24, F-13016 Marseille, France
*Author to whom correspondence should be addressed.
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