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Numerical analysis

The method of false position provides an exact solution for linear functions, but more direct algebraic techniques have supplanted its use for these functions. However, in numerical analysis, double false position became a root-finding algorithm used in iterative numerical approximation techniques.

Many equations, including most of the more complicated ones, can be solved only by iterative numerical approximation. This consists of trial and error, in which various values of the unknown quantity are tried. That trial-and-error may be guided by calculating, at each step of the procedure, a new estimate for the solution. There are many ways to arrive at a calculated-estimate and regula falsi provides one of these.

Given an equation, move all of its terms to one side so that it has the form, f (x) = 0, where f is some function of the unknown variable x. A value c that satisfies this equation, that is, f (c) = 0, is called a root or zero of the function f and is a solution of the original equation. If f is a continuous function and there exist two points a and b such that f (a) and f (b) are of opposite signs, then, by the intermediate value theorem, the function f has a root in the interval (a, b).

There are many root-finding algorithms that can be used to obtain approximations to such a root. One of the most common is Newton's method, but it can fail to find a root under certain circumstances and it may be computationally costly since it requires a computation of the function's derivative. Other methods are needed and one general class of methods are the two-point bracketing methods. These methods proceed by producing a sequence of shrinking intervals, at the k th step, such that (a, b) contains a root of f.