Bisection Technique

1. What?

   The first technique, based on the Intermediate Value Theorem, is called the Bisection, or Binary-search, method.

2. Why?

   Can be used to accelerate the convergence of a sequence that is linearly convergent,
   regardless of its origin or application.

3. Method:
   

4. Algorithm:
   Show Algorithm

5. Drawbacks:
   

   It is, relatively, slow to converge:
   (that is, N may become quite large before \(| p − p_N|\) is sufficiently small)
   and a good intermediate approximation might be inadvertently discarded

6. Stopping Criterions:
   

   The best criterion is (2.2)

7. Convergence:
   

   It Always converges to a solution!

8. Rate of Convergence \ Error Bound:
   
   

9. The problem of Percision:
   We use,
   

10. The Signum Function:
    We use,
    

11. MatLab Implementation: