|
週次 |
日期 |
單元主題 |
|
Week 1 |
09/15 |
No class (Mid-Autumn festival)
|
|
Week 1 |
09/13 |
Course overview & examples |
|
Week 2 |
09/20 |
Linear algebra review: Matrices & vectors |
|
Week 2 |
09/22 |
Linear algebra review: Norms |
|
Week 3 |
09/29 |
Linear algebra review: SVD |
|
Week 3 |
09/27 |
No class: Typhoon |
|
Week 4 |
10/06 |
QR factorization: Gram-Schmidt orthogonalization |
|
Week 4 |
10/04 |
Linear algebra review: SVD & four fundamental subspaces |
|
Week 5 |
10/13 |
Least squares problems |
|
Week 5 |
10/11 |
Householder transformation |
|
Week 6 |
10/18 |
Conditioning of linear system problems |
|
Week 6 |
10/15 |
Rank deficient least squares problems
& least-norm solution of undetermined linear system |
|
Week 7 |
10/25 |
Conditioning of eigenvalue problems & linear least squares problems |
|
Week 7 |
10/27 |
Stability of algorithms |
|
Week 8 |
11/03 |
No class (self-learning week) |
|
Week 8 |
11/01 |
Midterm exam |
|
Week 9 |
11/10 |
Stability of algorithm |
|
Week 9 |
11/08 |
No class (self-learning week) |
|
Week 10 |
11/17 |
Cholesky decomposition |
|
Week 10 |
11/15 |
Stability of algorithm, LU decomposition (3hrs makeup class for week 16) |
|
Week 11 |
11/24 |
Givens rotation & Householder reduction to Hessenberg form |
|
Week 11 |
11/22 |
Eigenvalue problems & overview of
eigenvalue algorithms |
|
Week 12 |
12/01 |
QR algorithm without shifts |
|
Week 12 |
11/29 |
Eigenvalue problems: examples,
& Rayleigh quotient & inverse iteration |
|
Week 13 |
12/08 |
Other eigenvalue algorithms ( Jacobi method, bisection,
& divided-and-conquer) |
|
Week 13 |
12/06 |
QR algorithm with shifts |
|
Week 14 |
12/15 |
GMRES (revised) |
|
Week 14 |
12/13 |
Computing SVD, iterative methods: simple iteration, & Arnoldi iteration |
|
Week 15 |
12/22 |
Conjugate gradient algorithm for SPD matrices: Derivation |
|
Week 15 |
12/20 |
Lanczos iteration \& conjugate gradient method |
|
Week 16 |
12/29 |
No class (travel abroad) |
|
Week 16 |
12/27 |
No class (travel abroad) |
|
Week 17 |
01/05 |
Biorthogonalization methods |
|
Week 17 |
01/03 |
Conjugate gradient algorithm: Convergence &
preconditioned conjugate gradient method |
|
Week 18 |
01/10 |
Final exam at Astro/Math 302 |