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