1. MAT 4725 Numerical Analysis Section 7.3 Iterative Techniques http://myhome.spu.edu/lauw

2. Maple Testing computer numbers 01v, 02v, 06v, 07vx, 11x, 12v, 16v and 17v.

3. Homework Induction – P(1) Basic algebraic proofs See me ….

4. Preview Focus on theoretical issues Jacobi Iterative Method

5. The need of iterative methods

6. Finding inverse… o Extremely expensive (time and storage) o More or less o Difficult/Impossible to implement in real time

7. Chapter 7 Iterative Techniques in Matrix Algebra Section 2.2 Fixed-Point Iteration

8. Chapter 7 Iterative Techniques in Matrix Algebra Section 7.3 Iterative Techniques

9. Section 2.2 Example 1 Show that if p is a fixed point of then p is a solution of

10. Idea

11. Example 1

13. Jacobi Iterative Method

14. Jacobi Iterative Method: Matrix Form

15. Convergence

16. Lemma c.f.

17. Theorem

18. HW

19. Corollary HW

20. Section 2.2 Corollary 2.4

21. Homework Download HW Read 8.2