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. For reading assignments, "MC" stands for "Matrix Computations," and "NLA" stands for "Numerical Linear Algebra."

Week
Date
Topic
Reading Slides Notes
1
Mon. 08/27
course overview; matrix notation and basic operations; vector spaces
NLA§1, MC§1.1
slides


Wed. 08/29 algorithmic considerations; orthogonality; vector and matrix norms NLA§2-3, MC§1.2, 2.2
slides
2
Mon. 09/03
No class (Labor day)



Wed. 09/05 matrix norms; singular value decomposition NLA§3-4, MC§2.3-4 slides
3
Mon. 09/10 more on SVD; projectors NLA§5-6 slides

Wed. 09/12 condition numbers; floating-point arithmetic NLA§12-13 slides HW#1 due
4
Mon. 09/17 accuracy and stability; triangular systems; backward stability of forward substitution NLA§14-15,17, MC§3.1 slides

Wed. 09/19 LU factorization; Gaussian elimination with partial pivoting
NLA§20-21, MC§3.2-3.4 slides
5
Mon. 09/24 accuracy and stability of Gaussian elimination
NLA§22, MC§3.5-4.1;
estimate condition number
slides

Wed. 09/26 positive definite systems; Cholesky factorization
NLA§23, MC§4.2-4 slides HW#2 due
6
Mon. 10/01 review for midterm #1; QR factorization, Gram-Schmidt orthogonalization NLA§7-8 slides

Wed. 10/03 Midterm #1 in class (covers up to Cholesky factorization)



7 Mon. 10/08 Fall Break: No classes in session



Wed. 10/10 Householder reflectors; Givens rotations; full-rank least squares problem NLA§10-11 slides
8 Mon. 10/15 conditioning of least squares problem; stability of Householder QR NLA§18,16 slides

Wed. 10/17 other methods for least squares problems; linear algebra software NLA§19 slides example C code
9 Mon. 10/22 eigenvalue problems; eigenvalue revealing factorizations NLA§24-25 slides HW#3 due

Wed. 10/24 reduction to Hessenberg forms; Rayleigh quotient iteration NLA§26-27 slides
10 Mon. 10/29 QR algorithm without shifts; QR algorithm with shifts NLA§28-29 slides

Wed. 10/31 more methods for tridiagonal problems NLA§30 slides
11 Mon. 11/05 sensitivity of eigenvalues; review for Midterm 2 MC§7.2 slides HW#4 due

Wed. 11/07 Midterm #2 in class (covers up to lecture on 10/31)


12 Mon. 11/12 Discussions of midterm #2



Wed. 11/14 computing SVD; sparse linear systems NLA§31; MC§11.1-11.2 slides
13 Mon. 11/19 Arnoldi and Lanczos iterations NLA§32-34 slides HW#5 due

Wed. 11/21 No class (Thanksgiving break) NLA§38, MC§11.3 slides
14 Mon. 11/26 conjugate gradient method



Wed. 11/28 minimal residual and generalized minimal residual methods NLA§35 slides
15 Mon. 12/03 biorthogonalization methods; other Krylov methods NLA§39; reference
slides

Wed. 12/05 preconditioners; multigrid methods NLA§40; MC§11.6 slides HW#6 due
16
Mon.12/10 Review for final exam

slides

17
Wed. 12/12
Final exam, 8:30pm--11:00pm