| Lecture |
Topics |
Remarks |
| Week 0 |
| Fri. 9/29 |
Stability Analysis
of Linear Systems (3.1) |
|
| Week 1 |
| Mon. 10/2 |
Solution of Triangular
Systems (3.2-3.3) |
|
| Wed. 10/4 |
Triangular Factorization
(3.3-3.4) |
|
| Fri. 10/6 |
Pivoting (3.5)
Iterative refinement (3.12) |
|
| Week 2 |
| Mon. 10/9 |
Gram Schmidt
QR factorization |
|
| Wed. 10/11 |
QR factorization
(3.3.4) and (5.6.1) |
|
| Fri. 10/13 |
QR factorization
(3.3.4) and (5.6.1) |
|
| Week 3 |
| Mon. 10/16 |
Linear Least Squares
(3.13) |
|
| Wed. 10/18 |
Linear Least Squares
(3.13) |
|
| Fri. 10/20 |
Singular Value
Decomposition (1.9) |
|
| Week 4 |
| Mon. 10/23 |
Eigenvalue Problem
Background (1.7-1.8) |
|
| Wed. 10/25 |
Schur Decomposition
Power Method (5.3) |
|
| Fri. 10/27 |
Rayleigh Quotient
Iteration |
|
| Week 5 |
| Mon. 10/30 |
Hessenberg Form
QR Algorithm (5.6)-(5.7) |
|
| Wed. 11/1 |
QR Algorithm
Sturm Sequences (5.10) |
|
| Fri. 11/3 |
Sturm Sequences (5.10)
Computing the SVD (5.8) |
|
| Week 6 |
| Mon. 11/6 |
Sparse Matrices (3.9) |
|
| Wed. 11/8 |
Graph Model
for Gaussian Elimination |
Sparse Matrix Paper0 |
| Fri. 11/10 |
|
Veterans Day Holiday |
| Week 7 |
| Mon. 11/13 |
Fill-in and
Ordering Algorithms |
Sparse Matrix Paper1 |
| Wed. 11/15 |
Iterative Methods
(4.1-4.2) |
|
| Fri. 11/17 |
Iterative Methods
(4.1-4.2) |
|
| Week 8 |
| Mon. 11/20 |
Work Estimates
Convergence |
|
| Wed. 11/22 |
|
|
| Fri. 11/24 |
|
Thanksgiving Holiday |
| Week 9 |
| Mon. 11/27 |
Conjugate Gradients
(4.3) |
|
| Wed. 11/29 |
Conjugate Gradients
(4.3) |
|
| Fri. 12/1 |
Preconditioned
Conjugate Gradients (4.3.5) |
|
| Week 10 |
| Mon. 12/4 |
Lanczos and
Biconjugate Gradients (4.4.3) |
|
| Wed. 12/6 |
Lanczos and
Biconjugate Gradients (4.5) |
BiCG Paper |
| Fri. 12/8 |
Review |
|
| Finals Week |
| Mon. 12/11 |
Office Hours 2:00-4:00 |
|
| Tues. 12/12 |
Final Exam, 11:30-2:30 |
|
