AMS 526 Lecture Schedule

Time: Monday & Wednesday 4:00 pm - 5:20 pm
Location: Physics P122

Note: All schedules are tentative and are subject to change.

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




* Rescheduled to 10/05 10:00--11:20am in Physics 125.
*
* Rescheduled to 10/12 10:00--11:20am in Physics 125.