Mastering Python for Finance - Second Edition

The secant method

The secant method uses secant lines to find the root. A secant line is a straight line that intersects two points of a curve. In the secant method, a line is drawn between two points on the continuous function, such that it extends and intersects the x axis. This method can be thought of as a Quasi-Newton method. By successively drawing such secant lines, the root of the function can be approximated.

The secant method is graphically represented in the following screenshot. An initial guess of the two x axis values, a and b, is required to find f(a) and f(b). A secant line, y, is drawn from f(b) to f(a) and intersects at the c point on the x axis, such that:

The solution to c is therefore as follows:

On the next iteration, ...