A GENERALIZED NEWTON-RAPHSON METHOD USING CURVATURE

Abstract

A numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton-Raphson method. The compared results between the proposed method and the Newton-Raphson method are listed. The proposed method has a wider convergent region of initial points and finds more proper solutions than the Newton-Raphson method. In particular, the paper proposes that the curvature method is replaced by the modified Newton method discussed by Ralston in dealing with multiple roots.