Schedule
This schedule should be considered tentative and subject to change, at least until it actually takes place! In addition to class notes, I have compiled some background notes that may be helpful.
| Week | Day | Date | Notes and readings | HW |
|---|---|---|---|---|
| Wed, | Jan 21 | Introduction |
||
| Fri, | Jan 23 | Matrix manipulations [Slides] |
||
| 2 | Mon, | Jan 26 | Linear algebra review |
|
| Wed, | Jan 28 | Linear algebra practice |
||
| Fri, | Jan 30 | Neumann series, sensitivity, conditioning |
||
| 3 | Mon, | Feb 02 | Floating point |
|
| Wed, | Feb 04 | Floating point |
||
| Fri, | Feb 06 | Gaussian elimination |
||
| 4 | Mon, | Feb 09 | Blocking |
|
| Wed, | Feb 11 | Perturbation theory, refinement, Cholesky |
||
| Fri, | Feb 13 | Pivoting, conditioning, error estimation |
||
| 5 | Mon, | Feb 16 | February break | |
| Wed, | Feb 18 | Sparse, banded, and structured solves (Bindel away) |
|
|
| Fri, | Feb 20 | Intro to least squares (Bindel away) |
||
| 6 | Mon, | Feb 23 | Least squares and QR |
|
| Wed, | Feb 25 | Ill-posedness and regularization |
||
| Fri, | Feb 27 | Ill-posedness and regularization |
||
| 7 | Mon, | Mar 02 | Applications of eigenvalue problems |
|
| Wed, | Mar 04 | Power iteration |
||
| Fri, | Mar 06 | From power methods to QR iteration |
||
| 8 | Mon, | Mar 09 | Hessenberg, tridiagonal, and bidiagonal |
|
| Wed, | Mar 11 | Stationary iterations |
||
| Fri, | Mar 13 | Gauss-Seidel convergence, extrapolation |
||
| 9 | Mon, | Mar 16 | Krylov subspace iterations (Bindel away) |
|
| Wed, | Mar 18 | Nonlinear equations in 1D (Bindel away) |
||
| Fri, | Mar 20 | Nonlinear equations in 1D (Bindel away) |
||
| 10 | Mon, | Mar 23 | Optimization in 1D |
|
| Wed, | Mar 25 | Nonlinear equations and optimization (Bindel away) |
||
| Fri, | Mar 27 | Newton in many dimensions |
||
| 11 | Mon, | Mar 30 | Spring break | |
| Wed, | Apr 01 | Spring break | ||
| Fri, | Apr 03 | Spring break | ||
| 12 | Mon, | Apr 06 | Gradient descent and Newton for optimization |
|
| Wed, | Apr 08 | Gauss-Newton and nonlinear least squares |
||
| Fri, | Apr 10 | Modified Newton iterations |
||
| 13 | Mon, | Apr 13 | Quasi-Newton and other iterations |
|
| Wed, | Apr 15 | Line search and globalization |
||
| Fri, | Apr 17 | Trust regions |
||
| 14 | Mon, | Apr 20 | Homotopy and continuation |
|
| Wed, | Apr 22 | Constraints and multipliers |
||
| Fri, | Apr 24 | Methods for equality constraints |
||
| 15 | Mon, | Apr 27 | Methods for inequality constraints |
|
| Wed, | Apr 29 | Derivative free methods |
||
| Fri, | May 01 | Stochastic optimizers |
||
| 16 | Mon, | May 04 | Review |