Bisection_Method

This is an iteration method based on Intermediate Value Theorem.

The bisection method is a root-finding method that applies to any continuous functions for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root. It is a very simple and robust method, but it is also relatively slow. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods.

Now, let a_k and b_k be the kth iterations then

m_k+1 = a_k + 1/2(b_k - a_k), k = 0,1,2...

(a_k+1, b_k+1) = (a_k, m_k+1) if f(a_k)*f(m_k+1) < 0

(a_k+1, b_k+1) = (m_k+1, b_k) if f(b_k)*f(m_k+1) < 0