Below is a tentative schedule of lectures. Schedule and topics are subject to change (probably not much)
|
topics |
week 1 (08/29 - 09/02) |
matrix-vector multiplication, orthogonal vectors and matrices |
week 2 (09/06 - 09) |
norms, the Singular Value Decomposition |
week 3 (09/12 - 16) |
projectors, QR factorization |
week 4 (09/19 - 23) |
Gram-Schmidt orthogonalization, householder triangularization, least squares problems |
week 5 (09/26 - 30) |
Gaussian elimination, pivoting |
week 6 (10/03 - 07) |
stability of Gaussian elimination, Cholesky factorization |
week 7 (10/10 - 14) |
eigenvalue problems, reduction of Hessenberg or tridiagonal form |
week 8 (10/17 - 21) |
midterm review, MT exam |
week 9 (10/24 - 28) |
Rayleigh quotient, inverse iteration |
week 10 (10/31 - 11/04) |
QR algorithm without shifts, QR algorithm with shifts
|
week 11 (11/07 - 11) |
other eigenvalue algorithms, computing the SVD |
week 12 (11/14 - 18) |
overview of iterative methods, conjugate gradients, preconditioning |
week 13 (11/21 - 23) |
Jacobi iteration, Gauss-Siedel iteration |
week 14 (11/28 - 12/02) |
SOR, other methods for linear systems |
week 15 (12/05 - 09) |
final exam review, final exam |