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

Abel Gomes and José Morgado

Mathematical Problems in Engineering, 2013, vol. 2013, 1-9

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, called generalized regula falsi (GRF) method to determine both zeros and extrema of a function. Consequently, it differs from the standard regula falsi method in that it is capable of finding any function zero in a given interval even when the Intermediate Value Theorem is not satisfied.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:394654

DOI: 10.1155/2013/394654

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