Secant’s method

This method is a modification of the Newton-Raphson’s method; since this is not necessary to calculate the derivative then you have the following expression.

f^' (x)=(f(x_(i-1) )-f(x_i))/(x_(i-1)-x_i ) (1)

Newton raphson

x_(i+1)= x_i-(f(x_i))/(f^' (x_i)) (2)

(1) in (2) Secante

x_(i+1)≈x_i-(f(x_i)(x_(i-1)-x_i ))/(f(x_(i-1))-f(x_i))

This expression is replaced in the Newton-Raphson’s equation and gives us the formula is called the secant method, and this is to approximate the slope of the straight line connecting the function evaluated at the point of study and at the point the previous iteration.

Example: