The secant method is a root-finding algorithm that approximates a function as linear in the region of interest and finds where the approximating line crosses the x-axis to estimate the next root. It only retains the most recent estimates, so the root may become unbracketed. When it converges, its order of convergence is quadratic.

1. Secant MethodA root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line crosses the axis. The secant method retains only the most recent estimate, so the root does not necessarily remain bracketed. The secant method is implemented in Mathematica as the undocumented option Method -> Secant in FindRoot[eqn, x, x0, x1].When the algorithm does converge, its order of convergence iswhere is a constant and is the golden ratio.so<br />