Root-finding algorithm

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In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called roots, of a function. A root of the function f is a number x such that f(x) = 0. As the zeros typically cannot be computed exactly, nor expressed in closed form, root-finding algorithms provide approximations to the zeros. The functions considered are typically continuous or, for most algorithms, differentiable. For real functions and complex functions, the approximations are commonly expressed as floating-point numbers, sometimes with error bounds. Solving an equation f(x) = g(x) is the same as finding the roots of the function h(x) = f(x) – g(x). Thus root-finding algorithms can be used to solve any equation of continuous functions. However, most root-finding algorithms do not guarantee that they will find all roots of a function, and if such an algorithm does not find any root, that does not necessarily mean that no root exists. Most numerical root-finding methods are iterative methods, producing...

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