Root-finding algorithm

Summary

A root-finding algorithm computes approximations of a zero of a function, that is, a point $x$ with $f(x) = 0$. Most such algorithms are iterative: they produce a sequence of points, or of shrinking intervals, that tends to a zero. Bracketing methods such as the bisection method and regula falsi keep a sign change and always converge for continuous $f$. Open methods such as Newton's method and the secant method converge faster near a simple zero, but only from good starting points. Methods are compared by their rate of convergence and by the number of function evaluations per step.