1. System of Linear Equations
Chapter 2
System of Linear Equations
Solving Linear Systems (2.4)
January 26, 2010
New TA (2 TAs)
Nejhum Shahed
Office Hours: 2-5pm Wed, E309

2. Elementary Elimination Matrices

3. Example: Gaussian Elimination

4. Example: Gaussian Elimination

5. Example: Gaussian Elimination

6. LU Factorization

7. LU Factorization

8. Example: LU Factorization

9. Example: LU Factorization
M1A=[1 2 2; ; ];
M2=[1 0 0;0 1 0; ]
M2M1A=[ 1 2 2; ; ];
L=[1 0 0;4 1 0; ];
What are M1, M1 A, M2 M2M1 A
A = LU, what are L and U ?

10. Row Interchanges

11. Partial Pivoting

12. LU Factorization with Partial Pivoting

13. Complete Pivoting

14. Example: Pivoting

15. Example: Small Pivots

16. Example, cont’d

17. Pivoting, cont’d

18. Residual

19. Residual

20. Example

21. Example

22. Uniqueness of LU Factorization

23. Complexity of Solving Linear Systems

24. Inversion vs. Factorization