TA:
Yijun Dong.
Email: ydong51432@gmail.com
Office hours: Mondays 11am - noon, Tuesdays 2pm - 3pm.
Zoom link for office hours is on canvas.
Meeting times:
Tuesdays and Thursdays, 9:30 - 10:45. GDC 4.304.
Website:
http://users.oden.utexas.edu/~pgm/Teaching/2021_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 the midterm exam, 40% for the 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 23) |
|
Thu: Review of basic concepts in linear algebra.
|
| 2 (Aug 30) |
|
Tue: Matrix operations (ch 1); orthonormal matrices (ch2). Thu: Vector norms and operator norms (ch 3). The matlab code used in class. |
| 3 (Sep 6) | Homework 1 due on Thursday. |
Tue: SVD (ch 4). Thu: SVD (ch 5). |
| 4 (Sep 13) |
Tue: SVD (ch5), projections (ch6). Thu: Projections (ch 6), QR factorization (ch 7). |
|
| 5 (Sep 20) | Homework 2 due on Thursday. |
Tue: Gram-Schmidt QR (ch 8). Code used in class. Thu: Householder QR (ch 10). Chapter 9 is part of prereqs. Please review as required. |
| 6 (Sep 27) |
|
Tue: Householder QR (ch 10). Thu: Least squares problems (ch 11). |
| 7 (Oct 4) | 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 11) |
|
Tue: Conditioning and stability (ch 12-15). Thu: Conditioning and stability (ch 12-15). |
| 9 (Oct 18) | Homework 4 due on Thursday. |
Tue: Stability of Householder QR (ch 16 - 17). Thu: Stability of least squares problems (ch 18 - 19). The matlab codes, 1 and 2, used in class. |
| 10 (Oct 25) |
|
Tue: Chapters 20 - 23. Thu: Midterm exam 9:00am-10:45am, in regular classroom. (The format of the exam depends on the covid situation.) The midterm covers Chapters 1 - 15. Exam. Solutions. |
| 11 (Nov 1) |
|
Tue: Chapters 20 - 23. Thu: Chapters 20 - 23. Codes: LU, conditioning of LU, LU and pivoting, Cholesky. |
| 12 (Nov 8) | Homework 5 due on Tuesday. |
Tue: Computing eigenvalues and eigenvectors. Thu: Computing eigenvalues and eigenvectors. |
| 13 (Nov 15) | Homework 6 due on Thursday. |
Tue: Computing eigenvalues and eigenvectors. Thu: Computing eigenvalues and eigenvectors. |
| 14 (Nov 22) |
|
Tue: Krylov methods. Thu: Thanksgiving. No class. |
| 15 (Nov 29) | Homework 7 due on Thursday. hw7p1.m; hw7p1_extra.m; hw7p2.m; hw7p3.m. |
Tue: Review. Thu: Review. Video lecture on conjugate gradients. Video lecture on Krylov methods for non-normal matrices. Video lecture on preconditioners. |
| 16 (Dec 6) |
|
Study week. |
| 17 (Dec 13) |
|
Final exam on Monday Dec 13, 9:00 - 12:00 (in the morning). |
Resources: