Given two successive approximations to a function’s root a, the secant method calculates where the secant through these two points
The secant method
meets the x-axis and uses this as the next approximation. So the iteration is given by
An iterative method for finding a root of the nonlinear equation f(x) = 0. It is given by the formula
where x0 and x1 are given starting values. This formula is derived by replacing f(x) by a straight line based on the last two iterates. Convergence is ultimately less rapid than for Newton’s method, but it can be overall more efficient on some problems since derivatives are not required.