2.2/

Fixed-Point Problems

1. Fixed Point:
2. Root-finding problems and Fixed-point problems:
   

   Root Finding and Fixed-point problems are

3. Why?:
   
4. Existence and Uniqueness of a Fixed Point.:
   

Fixed-Point Iteration

1. Approximating Fixed-Points:
   
2. Algorithm:
   
3. Convergence:
   • Fixed-Point Theorem:
     
   • Error bound in using \(p_n\) for \(p\):
     

     Notice:
     

4. Using Fixed-Points:
   

   Question: \(\ \ \ \ \\)

   Answer:
   

5. Newton’s Method as a Fixed-Point Problem: