Class | Date | Main Topic | Section(s) |
1, HW0 | M 01/29 | BQ0a, BQ0b, IQ0, Overview, GQ0a, pre-assessment | |
2, HW1 | W 01/31 | Gaussian elimination without row interchanges, GQ1a | 1.7 |
3 | M 02/05 | Gaussian Elimination (GE) and the LU Decomposition, GQ1b | 1.8 |
4, HW2 | W 02/07 | Roundoff Errors; Propagation of Roundoff Errors | 2.5, 2.6 |
5 | M 02/12 | Operation count for GE, pivoting, and triangular solves | |
6, HW3 | W 02/14 | Vector Norms | 2.1 |
7 | M 02/19 | Matrix Norms, GQ1d | 2.1 |
8, HW4 | W 02/21 | Sensitivity Analysis and Condition Numbers | 2.2, 2.3 |
9 | M 02/26 | A Posteriori Error Analysis; Backward Error Analysis of GE, GQ1e | 2.4, 2.7 |
10, HW5 | W 02/28 | Positive Definite Systems; Cholesky Decomposition; Sparse GE and Cholesky in Matlab | 1.4, 1.6, 1.9 |
11 | M 03/04 | Iterative Methods for Linear Systems; A Model Problem | 8.1 |
12, HW6 | W 03/06 | The Classical Iterative Methods | 8.2 |
13 | M 03/11 | Steepest Descent for linear systems, GQ2a | 8.4, 8.7 |
14, HW7 | W 03/13 | The CG Method, preconditioning, GQ2b | 8.7, 8.6, 8.10 |
M 03/18 | Spring Break | ||
W 03/20 | Spring Break | ||
15 | M 03/25 | Theory of classical iterative methods and the CG method | 8.3, 8.8, 8.9 |
16, HW8 | W 03/27 | Derivation and convergence of the CG Algorithm, GQ2c | 8.8, 8.9 |
17, HW9 | M 04/01 | Review of eigenvalues and diagonalization, GQ2d | 5.2 |
18 | W 04/03 | Midterm Exam | |
19, HW10 | M 04/08 | Diagonalization, complex matrices, notation, and motivation of QR factorization, GQ3a | 5.4 |
20 | W 04/10 | The discrete least squares problem and the QR factorization | 3.1-3.2 |
21, HW11 | M 04/15 | QR factorization and least squares problems | 3.2-3.3 |
22 | W 04/17 | The Singular Value Decomposition (SVD) | 4.1 |
23 | M 04/22 | Properties of the SVD | 4.2 |
24, HW12 | W 04/24 | The SVD and the Least Squares Problem | 4.3 |
25 | M 04/29 | The Power Method and Extensions | 5.3 |
26, HW13 | W 05/01 | Similarity transformation; reduction to Hessenberg form; the QR Algorithm | 5.5 |
27 | M 05/06 | Shifts in the QR Algorithm | 5.6 |
28, HW14 | W 05/08 | Computer numbers: IEEE-standard for floating-point numbers | |
29, HW15 | M 05/13 | Review, post-assessment | |
M 05/20 | 03:30-05:30 Final Exam Note the date and time! | ||