2.3/

Newton’s Method

1. What?:
   • Newton’s (or the Newton-Raphson) method is:
   • 
     
   • 
     
2. Derivation:
   
3. Algorithm:
   
4. Stopping Criterions:
   

Convergence using Newton’s Method

1. Convergence Theorem:
   Theorem:
   

   The crucial assumption is

   
   

   Theorem 2.6 states that,
   (1)
   

   (2)

The Secant Method

1. What?
   In Newton’s Method
   We approximate \(f'( p_n−1)\) as:
   

   To produce:
   

2. Why?
   

   \(\ \ \ \ \ \ \ \ \\):

   Frequently,

   Note:

3. Algorithm:
   
4. Convergence Speed:
   

The Method of False Position

1. What?
   
2. Why?
   
3. Method:
   
4. Algorithm: