A Generalized Regula Falsi Method for Finding Zeros and Extrema of Real Functions

Abstract

Many zero-finding numerical methods are based on the Intermediate Value Theorem, which states that a zero of a real function is bracketed in a given interval if and have opposite signs; that is, . But, some zeros cannot be bracketed this way because they do not satisfy the precondition . For example, local minima and maxima that annihilate may not be bracketed by the Intermediate Value Theorem. In this case, we can always use a numerical method for bracketing extrema, checking then whether it is a zero of or not. Instead, this paper introduces a single numerical method, calledgeneralized regula falsi(GRF) method to determine both zeros and extrema of a function. Consequently, it differs from the standardregula falsi methodin that it is capable of finding any function zero in a given interval even when the Intermediate Value Theorem is not satisfied.