Regula_Falsi_Method

Iteration method to find root of a function.

This method is based on the first degree equation.

Geometrically, in this method we replace the function f(x) by a straight line, l
or a chord passing through the points (x_k, f_k) and
(x_k-1, f_k-1) and take the point of intersection, x_k+1 of the straight line with the x-axis
as the next approximation to the root.

Equating slope of the line, m gives :
m = (f_k - f_k-1)/(x_k - x_k-1) = (-f_k)/(x_k+1 - x_k)
=> x_k+1 = x_k - (x_k - x_k-1)*f_k / (f_k - f_k-1)

If the approximations are such that f_k * f_k-1 < 0 then the method is known as Regula Falsi method.
For next iteration use :
x_k = x_k+1 if f_k * f_k-1 < 0
x_k-1 = x_k+1 if f_k * f_k-1 > 0