| Week |
Topics |
Complementary
Readings |
Notes |
| Sept 12, 14 |
Introduction, application of
sparse matrices, graph representation, data structures |
[Saad 2.1, 2.2,
3.2, 3.4, 3.5] [BBC+ 4.3] [DER 2.1-2.7, 2.12, 2.13] |
|
| Sept 19, 21 |
Graph theory, Gaussian
elimination & LU factorization, Doolittle form |
[DER 3.1-3.8] |
|
| Sept 26, 28 |
Stability, Pivoting, Conditioning |
[Saad 3.3] [DER 4.1-4.14] |
|
| Oct 3, 5 |
Sparse Gaussian elimination:
solve factor and analyze |
[Saad 3.6] [DER 5.1-5.8] |
A1 due (Oct 3) |
| Oct 10, 12 |
Ordering: RCM, min degree,
Markowitz criterion; Image denoising |
[Saad 3.3.3] [DER 7.1-7.8, 8.1-8.4] |
|
| Oct 17, 19 |
Iterative
methods: Richardson, Jacobi, Gauss-Seidel, SOR |
[Saad 4.1] [BBC+ 2.1, 2.2] |
|
| Oct 24, 26 |
Convergence analysis of
relaxation methods, Steepest descent |
[Schewchuck] [Saad 4.2, 5.3] [BBC+ 2.2] |
A2 due (Oct 24) |
| Oct 31, Nov 2 |
Conjugate gradient,
preconditioning |
[Schewchuck] [Saad 6.7, 9.2] [BBC+ 2.3.1, 3.1, 3.2, 3.3, 3.4] |
|
| Nov 7, 9 |
Incomplete LU
factorization, convergence analysis |
[Saad
6.11, 10.1-10.3] [BBC+ 3.4.2] |
|
| Nov 14, 16 |
Other preconditioners, Krylov
subspace methods |
[Saad
6.1-6.5, 7.1-7.4] [BBC+ 2.3.4, 2.3.5, 2.3.7, 2.3.8] |
A3 due (Nov 14) |
| Nov 21, 23 |
Markov decision processes,
policy iteration |
[Sutton
and Barto 4.1, 4.2, 4.3] |
|
| Nov 28, 30 |
Algebraic decision diagrams |
[Bahar
et al. 1993] |
|
| Dec 5 |
Review |
A4 due (Dec 5) |