TA:
James Levitt. Room: Email: jlevitt@oden.utexas.edu
Office hours: Tuesdays 13:00 - 14:30 and Wednesdays 14:00 - 15:30, POB 3.256
Meeting times:
Tuesdays and Thursdays, 9:30 - 11:00. GDC 4.304.
Website:
http://users.oden.utexas.edu/~pgm/Teaching/2019_NLA/
Syllabus:
pdf
Description:
Fast algorithms for solving linear algebraic problems form one of the
cornerstones of scientific and engineering computations, as well as in
machine learning and data analysis. In all of these areas, tasks such
as solving linear systems, computing eigenvectors and eigenvalues of
large matrices, solving linear regression problems, etc., often form the
core of large scale computations. The class will describe efficient techniques
for solving problems such as these. Both the theoretical
foundations of the methods, and practical considerations for how to implement
the methods efficiently will be covered.
The course will also discuss essential concepts of numerical analysis such as backwards and forwards errors, stability of numerical methods, and floating point arithmetic.
Examination:
35% for homeworks, 25% for midterms, 40% for final exam. See syllabus for details.
Late policy: The first time you hand in a homework late, you will get 70% credit provided that you hand your work in within 5 days of the due date. Any subsequent late homeworks will receive no credit.
Schedule: All future times are tentative!
| Week: |
Homework: |
Material covered: |
| 1 (Aug 26) |
|
Thu: Review of basic concepts in linear algebra.
|
| 2 (Sep 2) |
|
Tue: Matrix operations (ch 1); orthonormal matrices (ch2). Thu: Vector norms and operator norms (ch 3). The matlab code used in class. |
| 3 (Sep 9) | Homework 1 due on Thursday. |
Tue: SVD (ch 4). Thu: SVD (ch 5). |
| 4 (Sep 16) |
Tue: SVD (ch5), projections (ch6). Thu: Projections (ch 6), QR factorization (ch 7). |
|
| 5 (Sep 23) | Homework 2 due on Thursday. |
Tue: Gram-Schmidt QR (ch 8). Thu: Householder QR (ch 9). |
| 6 (Sep 30) |
|
Tue: Householder QR (ch 9). Thu: Least squares problems (ch 11). |
| 7 (Oct 7) | Homework 3 due on Thursday. |
Tue: Conditioning and stability (ch 12-15). The matlab code used in class. Thu: Conditioning and stability (ch 12-15). |
| 8 (Oct 14) |
|
Tue: Conditioning and stability (ch 12-15). Thu: Conditioning and stability (ch 12-15). The matlab codes, 1 and 2, used in class. |
| 9 (Oct 21) | Homework 4 due on Thursday. |
Tue: Stability of Householder QR (ch 16 - 17). Thu: Stability of least squares problems (ch 18 - 19). |
| 10 (Oct 28) |
|
Tue: Midterm exam 9:00am-10:45am, in regular classroom. The midterm covers Chapters 1 - 15. Exam, solutions. Thu: Chapters 20 - 23. |
| 11 (Nov 4) |
|
Tue: Chapters 20 - 23. Thu: Chapters 20 - 23. Codes: LU, conditioning of LU, LU and pivoting, Cholesky. |
| 12 (Nov 11) | Homework 5 due on Tuesday. |
Tue: Computing eigenvalues and eigenvectors. Thu: Computing eigenvalues and eigenvectors. |
| 13 (Nov 18) | Homework 6 due on Thursday. |
Tue: Computing eigenvalues and eigenvectors. Thu: Computing eigenvalues and eigenvectors. |
| 14 (Nov 25) |
|
Tue: Krylov methods. Slides. Thu: Thanksgiving. No class. |
| 16 (Dec 2) | Homework 7 due on Thursday. hw7p1.m; hw7p1_extra.m; hw7p2.m; hw7p3.m. |
Tue: Krylov methods. Thu: Krylov methods and review. Slides on Lanczos. Review slides. Video lecture on conjugate gradients. Video lecture on Krylov methods for non-normal matrices. Video lecture on preconditioners. |
| 17 (Dec 9) |
|
Final exam on Saturday Dec 14, 19:00 - 22:00. Room: BUR 136. Exam, solutions. Mean = median = 76. |
Resources: