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.

翻译：Regula Falsi,或假位置方法,是一种数字方法,用来寻找在一定间隔[a,b] 范围内f(x)=0(f)的近似解决办法,f(a,b)是[a,b]和f(a)f(f)f(b) < 0.]上的实际价值连续函数。以往的研究证明,在f(f)的某些假设下,这一方法趋于一致,例如f(f)的第一和第二衍生物不会改变[a,b]间隔上的符号。在本文中,我们删除这些假设,并证明所有连续功能的方法趋同。