The convergence of the Regula Falsi method

TL;DR

This paper proves the convergence of the Regula Falsi method for all continuous functions, removing previous restrictions on the function's derivatives, thus broadening its applicability.

Contribution

It establishes the convergence of the Regula Falsi method without assumptions on the derivatives of the function, extending prior results.

Findings

Proves convergence for all continuous functions

Removes derivative sign change restrictions

Broadens applicability of the Regula Falsi method

Abstract

Regula Falsi, or the method of false position, is a numerical method for finding an approximate solution to f(x) = 0 on a finite interval [a, b], where f is a real-valued continuous function on [a, b] and satisfies f(a)f(b) < 0. Previous studies proved the convergence of this method under certain assumptions about the function f, such as both the first and second derivatives of f do not change the sign on the interval [a, b]. In this paper, we remove those assumptions and prove the convergence of the method for all continuous functions.