| Lecture |
Date |
Topics |
Complementary
Readings |
| 1 |
May 3 |
Introduction, LU
factorization (Lecture
slides) |
[TB] Chapter 1, pages 1-10 [TB] Chapter 20, pages 147-152 |
| 2 |
May 5 |
Cholesky factorization, tridiagonal, band matrices (Lecture slides) | [TB] Chapter 23, pages
172-176 |
| 3 |
May 10 |
1D, 2D Laplacian (Lecture slides) |
[Saad]
Chapter 2 |
| 4 |
May 12 |
Sparse Gaussian Elimination,
graph representation (Lecture
slides) |
[Saad] Sect 3.1-3.2 |
| 5 |
May 17 |
Ordering methods (Lecture slides) |
[Saad] Sect 3.3 |
| 6 |
May 19 |
Stability and image denoising
(Lecture slides) |
[TB] Chapter 22, pages 163-170 |
| 7 |
May 24 |
Image denoising and iterative
methods (lecture slides) |
|
| May 25 |
Assignment 1 due (11:59 pm) |
||
| 8 |
May 26 |
Iterative methods and
steepest descent (Lecture
slides) |
[Saad]
Chapter 4 |
| 9 |
May 31 |
Conjugate gradient (Lecture slides) |
[TB] Chapter 38, pages
293-301 [Saad] Sect 5.3 and 6.7 |
| 10 |
June 2 |
Least squares problems (Lecture slides) |
[TB] Chapter 11 |
| 11 |
June 7 |
QR Factorization and
Gram-Schmidt orthogonalization (Lecture slides) |
[TB] Chapters 7, 8 |
| 12 |
June 9 |
Householder reflections and
Givens rotations (Lecture
slides) |
[TB] Chapter 10 |
| June 13 |
Assignment 2 due (11:59 pm) |
||
| 13 |
June 14 |
Singular value decomposition
and conditioning (Lecture
slides) |
[TB] Chapters 4, 12 |
| 14 |
June 16 |
Eigenvalue problems (Lecture slides) |
[TB] Chapter 24, 25, 26 |
| 15 |
June 21 |
Midterm (in class)
|
|
| 16 |
June 23 |
Rayleigh Quotient Algorithm
and QR Algorithm (Lecture
slides) |
[TB] Chapter 27, 28 |
| 17 |
June 28 |
QR algorithm and reduction to
Hessenberg (Lecture
slides) |
[TB] Chapter 28 |
| 18 |
June 30 |
QR method with shifts, Google
PageRank (Lecture
slides) |
[TB] Chapter 29 |
| July 4 |
Assignment 3 due (11:59 pm) |
||
| 19 |
July 5 |
Singular value decomposition
(Lecture slides) |
[TB] Chapter 31 |
| 20 |
July 7 |
Bidiagonalization, SVD Image
Compression (Lecture
slides) |
[TB] Chapter 31 |
| 21 |
July 12 |
Information retrieval using SVD (Lecture slides) | |
| 22 |
July 14 |
Application: regression in
machine learning (Lecture
slides) |
|
| 23 |
July 19 |
Principal component analysis,
eigenfaces (Lecture
slides) |
|
| July 20 |
Assignment 4 due (11:59 pm) |
||
| 24 |
July 21 |
Open problems (Lecture slides) |