A SIMPLE AND EFFICIENT ROOT-FINDING ALGORITHM FOR DEALING WITH SCALAR NONLINEAR EQUATIONS: ITERATIVE PROCEDURE BASED ON GEOMETRIC CONSIDERATIONS
GREGORY ANTONI *
Aix-Marseille Universite, IFSTTAR, LBA UMR T24, F-13016 Marseille, France
*Author to whom correspondence should be addressed.
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