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Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)

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. Elementary Elimination Matrices. Example: Gaussian Elimination. Example: Gaussian Elimination. Example: Gaussian Elimination. LU Factorization.

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Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)

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  1. 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 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

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