1. ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 19 Solution of Linear System of Equations - Iterative Methods

2. Last Time-Matrix Inversion

3. [A][A] -1 [A] [A] -1 =[I] If [A] -1 does not exist [A] is singular

4. Last Time-Matrix Inversion

5. Solution

6. Last Time-Matrix Inversion [A] [A] -1 =[I]

7. Last Time-Matrix Inversion

10. Iterative Methods Recall Techniques for Root finding of Single Equations Initial Guess New Estimate Error Calculation Repeat until Convergence

11. Gauss Seidel

12. First Iteration: Better Estimate

13. Gauss Seidel Second Iteration: Better Estimate

14. Gauss Seidel Iteration Error: Convergence Criterion:

15. Jacobi Iteration

16. First Iteration: Better Estimate

17. Jacobi Iteration Second Iteration: Better Estimate

18. Jacobi Iteration Iteration Error:

19. Homework 11.7 – Use MathCAD to implement Gauss Seidel Iterations 12.14 – Use EXCEL to calculate Inverse Matrix and Solve Equations