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 |
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| Wed, | Jan 21 | Introduction |
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| Fri, | Jan 23 | Matrix manipulations [Slides] |
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| 2 | Mon, | Jan 26 | Linear algebra review |
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| Wed, | Jan 28 | Linear algebra practice |
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| Fri, | Jan 30 | Neumann series, sensitivity, conditioning |
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| 3 | Mon, | Feb 02 | Floating point |
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| Wed, | Feb 04 | Sums, dots, and triangle solves |
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| Fri, | Feb 06 | Gaussian elimination |
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| 4 | Mon, | Feb 09 | Blocked LU and Cholesky |
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| Wed, | Feb 11 | GEPP, backward error analysis, refinement |
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| Fri, | Feb 13 | Beyond linear solves + structured solves |
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| 5 | Mon, | Feb 16 | February break | |
| Wed, | Feb 18 | Sparse solves (Bindel away) [Slides] |
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| Fri, | Feb 20 | Intro to least squares (Bindel away) |
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| 6 | Mon, | Feb 23 | Least squares and QR |
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| Wed, | Feb 25 | Ill-posedness and regularization |
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| Fri, | Feb 27 | Ill-posedness and regularization |
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| 7 | Mon, | Mar 02 | Applications of eigenvalue problems |
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| Wed, | Mar 04 | Power iteration |
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| Fri, | Mar 06 | From power methods to QR iteration |
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| 8 | Mon, | Mar 09 | Hessenberg, tridiagonal, and bidiagonal |
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| Wed, | Mar 11 | Stationary iterations |
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| Fri, | Mar 13 | Gauss-Seidel convergence, extrapolation |
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| 9 | Mon, | Mar 16 | Krylov subspace iterations (Bindel away) |
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| Wed, | Mar 18 | Nonlinear equations in 1D (Bindel away) |
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| Fri, | Mar 20 | Nonlinear equations in 1D (Bindel away) |
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| 10 | Mon, | Mar 23 | Optimization in 1D |
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| Wed, | Mar 25 | Nonlinear equations and optimization (Bindel away) |
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| Fri, | Mar 27 | Fixed point iterations and Newton |
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| 11 | Mon, | Mar 30 | Spring break | |
| Wed, | Apr 01 | Spring break | ||
| Fri, | Apr 03 | Spring break | ||
| 12 | Mon, | Apr 06 | Solvers on an autocatalytic example [Slides] |
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| Wed, | Apr 08 | Gradient descent and Newton for optimization |
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| Fri, | Apr 10 | Gauss-Newton and nonlinear least squares |
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| 13 | Mon, | Apr 13 | Modified Newton iterations |
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| Wed, | Apr 15 | Quasi-Newton and other iterations |
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| Fri, | Apr 17 | Line search and globalization |
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| 14 | Mon, | Apr 20 | Trust regions |
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| Wed, | Apr 22 | Homotopy and continuation |
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| Fri, | Apr 24 | Constraints and multipliers |
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| 15 | Mon, | Apr 27 | Methods for equality constraints |
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| Wed, | Apr 29 | Methods for inequality constraints |
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| Fri, | May 01 | Derivative free methods |
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| 16 | Mon, | May 04 | Review |
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| Sat, | May 09 | Final exam at 2 PM |