AMS 526 Lecture Schedule

Week Date Topic Reading Slides Notes
1 Mon. 08/28 course overview; matrix notation and basic operations; vector spaces NLA§1, MC§1.1 slides
Wed. 08/30 algorithmic considerations; orthogonality NLA§2, MC§1.2 slides
2 Mon. 09/04 No class (Labor Day)
Wed. 09/06 vector and matrix norms NLA§3, MC§2.2–4 slides
3 Mon. 09/11 singular value decomposition NLA§4–5 slides
Wed. 09/13 projectors; condition numbers NLA§6,12 slides HW#1 due (Fri.)
4 Mon. 09/18 floating-point arithmetic; accuracy and stability NLA§13–15 slides
Wed. 09/20 triangular systems; backward stability of forward substitution NLA§17, MC§3.1 slides
5 Mon. 09/25 Gaussian elimination with partial pivoting NLA§20–21, MC§3.2&3.4 slides
Wed. 09/27 conditioning and stability of Gaussian elimination NLA§22, MC§3.3&3.5 slides HW#2 due (Fri.)
6 Mon. 10/02 positive definite systems; Cholesky factorization; review for midterm #1 NLA§23, MC§4.2 slides
Wed. 10/04 Midterm #1 in class (covers up to Cholesky factorization)
7 Mon. 10/09 No class (Fall break)
Wed. 10/11 QR factorization, Gram-Schmidt orthogonalization; Householder reflectors NLA§7,8,10 slides
8 Mon. 10/16 Givens rotations; full-rank least squares problem; conditioning of least squares problem NLA§11,18 slides
Wed. 10/18 stability of Householder QR; other methods for least squares problems; linear algebra software NLA§16,19; example C code slides HW#3 due (Fri.)
9 Mon. 10/23 eigenvalue problems; eigenvalue revealing factorizations NLA§24–25 slides
Wed. 10/25 reduction to Hessenberg forms; Rayleigh quotient iteration NLA§26–27 slides
10 Mon. 10/30 QR algorithm without shifts; QR algorithm with shifts NLA§28–29 slides
Wed. 11/01 more methods for tridiagonal problems NLA§30 slides HW#4 due (Fri.)
11 Mon. 11/06 sensitivity of eigenvalues; review for midterm #2 MC§7.2 slides
Wed. 11/08 Midterm #2 in class (covers up to more methods for tridiagonal problems)
12 Mon. 11/13 computing SVD; sparse storage formats NLA§31 slides
Wed. 11/15 sparse direct solvers; overview of iterative methods MC§11.1–11.2 slides
13 Mon. 11/20 Arnoldi and Lanczos iterations NLA§32–34 slides HW#5 due (Sun.)
Wed. 11/22 No class (Thanksgiving break)
14 Mon. 11/27 conjugate gradient method NLA§38; MC§11.3 slides
Wed. 11/29 minimal residual and generalized minimal residual methods NLA§35 slides
15 Mon. 12/04 biorthogonalization methods; other Krylov methods; preconditioners NLA§39–40; reference slides
Wed. 12/06 a brief introduction to multigrid methods MC§11.6 slides HW#6 due (Sun.)
16 Mon. 12/11 Review for final exam slides
Tue. 12/12 Final exam, 8:30pm–11:00pm (Light Engineering 154)

Abbreviations

MC:
Matrix Computations

NLA:
Numerical Linear Algebra


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