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

Abstract EN

Many zero-finding numerical methods are based on the Intermediate Value Theorem, which states that a zero of a real function f:ℝ→ℝ is bracketed in a given interval A,B⊂ℝ if fA and fB have opposite signs; that is, fA·fB<0.

But, some zeros cannot be bracketed this way because they do not satisfy the precondition fA·fB<0.

For example, local minima and maxima that annihilate f 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 f 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 A,B⊂ℝ even when the Intermediate Value Theorem is not satisfied.