Week |
Lecture |
Notes |
1 |
| Aug 24 |
No Class |
| Aug 26 |
Introduction |
| Aug 28 |
Matrix Vector Products |
|
|
2 |
| Aug 31 |
Diags, Permutations, Kron |
| Sep 2 |
Norms, SVD |
| Sep 4 |
Fast Transforms |
|
|
3 |
| Sep 7 |
No Class |
| Sep 9 |
Condition & Floating Point |
| Sep 11 |
LU Factorization |
|
| |
| 2.6, 2.7
A1 Due 9/9 |
| 3.1, 3.2 |
|
4 |
| Sep 14 |
Roundoff & Pivoting |
| Sep 16 |
Condition Estimation |
| Sep 18 |
Positive Definite Systems |
|
|
5 |
| Sep 21 |
Banded Systems |
| Sep 23 |
Block Structured Systems |
| Sep 25 |
Fast Poisson Solvers |
|
| 4.3 |
| 4.5, 12.3
A2 Due 9/23 |
| 4.8 |
|
6 |
| Sep 28 |
Sparse Lin System Solvers |
| Sep 30 |
Conjugate Gradients |
| Oct 2 |
Preconditioning |
|
|
7 |
| Oct 5 |
Orthogonal Trans |
| Oct 7 |
The QR Factorization |
| Oct 9 |
Linear Least Squares |
|
|
|
8 |
| Oct 12 |
No Class |
| Oct 14 |
Rank Deficient Problems |
| Oct 16 |
Constrained LS |
|
|
|
9 |
| Oct 19 |
Subspace Computations |
| Oct 21 |
Total Least Squares |
| Oct 23 |
|
|
| 6.4 |
| 6.3 |
| 11.4
A4 Due 10/23 |
|
|
10 |
| Oct 26 |
Symmetric Eigenproblem |
| Oct 28 |
No Class |
| Oct 30 |
Jacobi Methods |
|
| 8.1, 8.2 |
| Take-Home Midterm (10/26-10/30) |
| 8.5 |
|
|
11 |
| Nov 2 |
Methods for Tridiag Probs |
| Nov 4 |
Lanczos Method |
| Nov 6 |
SVD Methods, Sparse LS |
|
| 8.3, 8.4 |
| 10.1, 10.3 |
| 8.6, 10.4, 11.4 |
|
|
12 |
| Nov 9 |
Unsymmetric Eigenproblem |
| Nov 11 |
Power Iterations |
| Nov 13 |
Hessenberg Reduction |
|
| 7.1, 7.2
A5 Due 11/9 |
| 7.3 |
| 7.4 |
|
|
13 |
| Nov 16 |
Schur Form |
| Nov 18 |
Arnoldi Method |
| Nov 20 |
Matrix Functions |
|
|
|
14 |
| Nov 23 |
Matrix Exponential |
| Nov 25 |
No Class |
| Nov 27 |
No Class |
|
|
|
15 |
| Nov 30 |
Toeplitz Systems |
| Dec 2 |
Structured Rank Problems |
| Dec 4 |
Multigrid |
|
|
