| Lecture |
Date |
Topics |
Complementary
Readings |
Notes |
| 1 |
Sept 13 |
Introduction, LU factorization (Lecture slides) |
[TB] Chapter 1, pages 1-10 [TB] Chapter 20, pages 147-152 |
|
| 2 |
Sept 15 |
Cholesky factorization, tridiagonal, band matrices (Lecture slides) | [TB] Chapter 12. pages 172-176 |
|
| 3 |
Sept 20 |
1D, 2D Laplacian (Lecture slides) |
[Saad] Chapter 2
|
A1 out |
| 4 |
Sept 22 |
Sparse Gaussian Elimination,
graph representation (Lecture slides) |
[Saad] Sect 3.1-3.2 | |
| 5 |
Sept 27 |
Ordering methods (Lecture slides) |
[Saad] Sect 3.3 | |
| 6 |
Sept 29 |
Stability and image denoising (Lecture slides) |
[TB] Chapter 22, pages 163-170 | |
| 7 |
Oct 4 |
Image denoising and iterative
methods (Lecture slides) |
|
|
| 8 |
Oct 6 |
Iterative methods and steepest
descent (Lecture slides) |
[Saad] Chapter 4 |
A1 due A2 out |
| 9 |
Oct 11 |
Conjugate
gradient (Lecture slides) |
[TB] Chapter 38, pages 293-301 [Saad] Sect 5.3 and 6.7 |
|
| 10 |
Oct 13 |
Least squares problems (Lecture slides) |
[TB] Chapter 11 | |
| 11 |
Oct 18 |
QR Factorization and
Gram-Schmidt orthogonalization (Lecture
slides) |
[TB] Chapters 7, 8 | |
| 12 |
Oct 20 |
Householder reflections and
Givens rotations (Lecture slides) |
[TB] Chapter 10 | |
| 13 |
Oct 25 |
Singular value decomposition and
conditioning (Lecture slides) |
[TB] Chapters 4, 12 | A2 due A3 out |
| 14 |
Oct 27 |
Eigenvalue problems (Lecture slides) | [TB] Chapter 24, 25, 26 | |
| 15 |
Nov 1 |
Rayleigh Quotient Algorithm and
QR Algorithm (Lecture slides) |
[TB] Chapter 27, 28 | |
| Midterm |
Nov 3 |
|||
| 17 |
Nov 8 |
QR algorithm and reduction to
Hessenberg (Lecture slides) |
[TB] Chapter 28 | |
| 18 |
Nov 10 |
QR method with shifts, Google
PageRank (Lecture slides) |
[TB] Chapter 29 | |
| Midterm review |
Nov 15 |
A3 due A4 out |
||
| 20 |
Nov 17 |
Singular value decomposition (Lecture slides) |
[TB] Chapter 31 |
|
| 21 |
Nov 22 |
Bidiagonalization, SVD Image
Compression (Lecture slides) |
[TB] Chapter 31 |
|
| 22 |
Nov 24 |
Search engine using SVD (Lecture slides) |
||
| 23 |
Nov 29 |
Convergence of iterative methods
(Lecture slides) |
||
| 24 |
Dec 1 |
Convergence of conjugate
gradient (Lecture slides) |
A4 due |