Week | Date | Topic | Reading | Slides | Notes |
---|---|---|---|---|---|
1 | Mon. 08/28 | course overview; matrix notation and basic operations; vector spaces | NLA§1, MC§1.1 | slides | |
Wed. 08/30 | algorithmic considerations; orthogonality | NLA§2, MC§1.2 | slides | ||
2 | Mon. 09/04 | No class (Labor Day) | |||
Wed. 09/06 | vector and matrix norms | NLA§3, MC§2.2–4 | slides | ||
3 | Mon. 09/11 | singular value decomposition | NLA§4–5 | slides | |
Wed. 09/13 | projectors; condition numbers | NLA§6,12 | slides | HW#1 due (Fri.) | |
4 | Mon. 09/18 | floating-point arithmetic; accuracy and stability | NLA§13–15 | slides | |
Wed. 09/20 | triangular systems; backward stability of forward substitution | NLA§17, MC§3.1 | slides | ||
5 | Mon. 09/25 | Gaussian elimination with partial pivoting | NLA§20–21, MC§3.2&3.4 | slides | |
Wed. 09/27 | conditioning and stability of Gaussian elimination | NLA§22, MC§3.3&3.5 | slides | HW#2 due (Fri.) | |
6 | Mon. 10/02 | positive definite systems; Cholesky factorization; review for midterm #1 | NLA§23, MC§4.2 | slides | |
Wed. 10/04 | Midterm #1 in class (covers up to Cholesky factorization) | ||||
7 | Mon. 10/09 | No class (Fall break) | |||
Wed. 10/11 | QR factorization, Gram-Schmidt orthogonalization; Householder reflectors | NLA§7,8,10 | slides | ||
8 | Mon. 10/16 | Givens rotations; full-rank least squares problem; conditioning of least squares problem | NLA§11,18 | slides | |
Wed. 10/18 | stability of Householder QR; other methods for least squares problems; linear algebra software | NLA§16,19; example C code | slides | HW#3 due (Fri.) | |
9 | Mon. 10/23 | eigenvalue problems; eigenvalue revealing factorizations | NLA§24–25 | slides | |
Wed. 10/25 | reduction to Hessenberg forms; Rayleigh quotient iteration | NLA§26–27 | slides | ||
10 | Mon. 10/30 | QR algorithm without shifts; QR algorithm with shifts | NLA§28–29 | slides | |
Wed. 11/01 | more methods for tridiagonal problems | NLA§30 | slides | HW#4 due (Fri.) | |
11 | Mon. 11/06 | sensitivity of eigenvalues; review for midterm #2 | MC§7.2 | slides | |
Wed. 11/08 | Midterm #2 in class (covers up to more methods for tridiagonal problems) | ||||
12 | Mon. 11/13 | computing SVD; sparse storage formats | NLA§31 | slides | |
Wed. 11/15 | sparse direct solvers; overview of iterative methods | MC§11.1–11.2 | slides | ||
13 | Mon. 11/20 | Arnoldi and Lanczos iterations | NLA§32–34 | slides | HW#5 due (Sun.) |
Wed. 11/22 | No class (Thanksgiving break) | ||||
14 | Mon. 11/27 | conjugate gradient method | NLA§38; MC§11.3 | slides | |
Wed. 11/29 | minimal residual and generalized minimal residual methods | NLA§35 | slides | ||
15 | Mon. 12/04 | biorthogonalization methods; other Krylov methods; preconditioners | NLA§39–40; reference | slides | |
Wed. 12/06 | a brief introduction to multigrid methods | MC§11.6 | slides | HW#6 due (Sun.) | |
16 | Mon. 12/11 | Review for final exam | slides | ||
Tue. 12/12 | Final exam, 8:30pm–11:00pm (Light Engineering 154) |
Notes: All schedules are tentative and are subject to change.