Muller's Method Algorithm

Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) equals zero, first presented by David E. Muller in 1956. It proceeds by a third-order recurrence relation similar to the second-order recurrence of the secant method, but where the secant method constructs a line through the last two approximations and uses the line's root as the next approximation, Muller's method uses the last three approximations to construct a parabola and uses a root of that parabola as the next approximation.