| Lecture |
Date |
Topics |
Complementary
Readings |
Notes |
| 1 |
Sept 14 |
Introduction, LU factorization |
[TB] Chapter 1, pages 1-10 [TB] Chapter 20, pages 147-152 |
|
| 2 |
Sept 16 |
1D, 2D Laplacian |
[Saad] Chapter 2 |
|
| 3 |
Sept 21 |
Cholesky factorization, tridiagonal, band matrices | [TB] Chapter 23, pages 172-176 | A1 out |
| no lecture |
Sept 23 |
|
||
| 4 |
Sept 28 |
Sparse Gaussian Elimination,
graph representation |
[Saad] Sect
3.1-3.2 |
|
| 5 |
Sept 30 |
Ordering methods |
[Saad] Sect 3.3 | |
| 6 |
Oct 5 |
Stability |
[TB] Chapter 22, pages 163-170 |
|
| 7 |
Oct 7 |
Image denoising |
||
| 8 |
Oct 12 |
Iterative methods |
[Saad] Chapter 4 |
A1 due A2 out |
| 9 |
Oct 14 |
Steepest descent and conjugate
gradient |
[TB] Chapter 38, pages 293-301 [Saad] Sect 5.3 and 6.7 |
|
| 10 |
Oct 19 |
Least squares problems |
[TB] Chapter 11 |
|
| 11 |
Oct 21 |
Gram-Schmidt orthogonalization |
[TB] Chapter 8 |
|
| 12 |
Oct 26 |
QR factorization |
[TB] Chapter 7 |
|
| 13 |
Oct 28 |
Householder transformation |
[TB] Chapter 10 |
|
| 14 |
Nov 2 |
Eigenvalue problems, Schur form | [TB] Chapter 24-25 |
A2 due A3 out |
| 15 |
Nov 4 |
Reduction to Hessenberg | [TB] Chapter 26 |
|
| Midterm | Nov 9 |
|||
| 16 |
Nov 11 |
Power iteration, inverse
iteration |
[TB] Chpater 27 |
|
| 17 |
Nov 16 |
QR method with shifts, Google
PageRank |
[TB] Chapter 28-29 |
|
| 18 |
Nov 18 |
Singular value decomposition |
[TB] Chapter 31 |
A3 due A4 out |
| 19 |
Nov 23 |
Bidiagonalization |
||
| 20 |
Nov 25 |
Search engine using SVD |
||
| 21 |
Nov 30 |
Convergence of iterative methods |
||
| 22 |
Dec 2 |
Preconditioning techniques |
A4 due |