Week
|
Date
|
Topic
|
Reading |
Slides |
Notes
|
1
|
Mon. 08/27
|
Course overview; matrix-matrix multiplication
|
§1.1 |
Lecture 1
|
|
|
Wed. 08/29 |
System of linear equations; Triangular systems
|
§1.2-1.3 |
Lecture 2 |
|
2
|
Mon. 09/03
|
No class
|
|
|
|
|
Wed. 09/05 |
Positive definite systems; Cholesky factorization; banded positive
definite systems
|
§1.4-1.5 |
Lecture 3 |
|
3
|
Mon. 09/10 |
Gaussian elimination and LU factorization |
§1.7-1.8 |
Lecture 4 |
|
|
Wed. 09/12 |
Sparse linear systems and
factorization methods |
§1.6,1.9 |
Lecture 5 |
HW#1 due |
4
|
Mon. 09/17 |
Vector and matrix norms; condition numbers
|
§2.1-2.2 |
Lecture 6 |
|
|
Wed. 09/19 |
Sensitivity of linear systems; a posteriori error analysis
using residual
|
§2.2-2.4 |
Lecture 7 |
|
5
|
Mon. 09/24 |
Floating point arithmetic; accuracy and stability
|
§2.5-2.6 |
Lecture 8 |
|
|
Wed. 09/26 |
Backward error analysis of Gaussian elimination; scaling |
§2.7-2.8 |
Lecture 9 |
HW#2 due |
6
|
Mon. 10/01 |
Component-wise sensitivity analysis; review
|
§2.9 |
Lecture 10 |
|
|
Wed. 10/03 |
Midterm 1 (covers §1.1--§2.8) in class
|
|
|
|
7
|
Mon. 10/08 *
|
Orthogonal Matrices; projectors; Linear least squares problems |
§3.1-2 |
Lecture 11 |
|
|
Wed. 10/10 **
|
QR factorization; Gram-Schmidt process
|
§3.3-4 |
Lecture 12 |
HW#3 due
|
8
|
Mon. 10/15 |
Geometric approach; updating QR factorization |
§3.5-6 |
Lecture 13 |
|
|
Wed. 10/17 |
Solution of Least Squares Problems; Singular-value decomposition
|
§4.1-2 |
Lecture 14 |
|
9
|
Mon. 10/22 |
SVD and least squares problem; sensitivity of least squares
problem
|
§4.3-4 |
Lecture 15
|
|
|
Wed. 10/24 |
Power method and similarity transformations
|
§5.2-4 |
Lecture 16 |
HW#4 due |
10
|
Mon. 10/29 |
class cancelled due to aftermath of Hurricane Sandy
|
|
|
|
|
Wed. 10/31 |
class cancelled due to aftermath of
Hurricane Sandy |
|
|
|
11
|
Mon. 11/05
|
Reduction to
Hessenberg and tridiagonal forms
|
§5.5-6 |
Lecture 17 |
|
|
Wed. 11/07 |
review for midterm #2; QR algorithm with shift;
Simultaneous iteration |
§5.6; 6.2 |
Lecture 18
|
reading |
12
|
Mon. 11/12 |
Midterm 2 (covers
§2.9--§5.5) in
class |
|
|
|
|
Wed. 11/14 |
SVD revisited; software for linear algebra |
§5.8 |
Lecture 19
|
|
13
|
Mon. 11/19 |
Other eigenvalue algorithms; Krylov subspaces; Arnoldi and Lanczos
iterations
|
§6.3-6.4 |
Lecture 20 |
HW#5 due |
|
Wed. 11/21 |
No class
|
|
|
reading
|
14
|
Mon. 11/26 |
Sensitivity of eigenvalues and eigenvectors; Conjugate gradient
method |
§7.1 |
Lecture 21 |
|
|
Wed. 11/28 |
More on conjugate gradient method; GMRES |
§8.4;8.7
|
Lecture 22 |
|
15
|
Mon. 12/03 |
Other Krylov subspace methods; Multigrid methods |
§8.10 |
Lecture 23 |
|
|
Wed. 12/05 |
Review
for final exam
|
§8.6 |
review
|
HW#6 due |
16-17
|
Tue. 12/11
|
Final exam, 8:30pm--11:00pm
in Physics P122
|
|
|
|