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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| 2 | Mon, | Jan 24 | Introduction |
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| Wed, | Jan 26 | Matrix manipulations |
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| Fri, | Jan 28 | Vector spaces, norms, singular values |
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| 3 | Mon, | Jan 31 | Matrices, norms, sensitivity and conditioning |
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| Wed, | Feb 02 | Matrices, norms, sensitivity and conditioning |
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| Fri, | Feb 04 | Snow day (was to be floating point) |
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| 4 | Mon, | Feb 07 | Floating point |
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| Wed, | Feb 09 | Gaussian elimination and Cholesky |
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| Fri, | Feb 11 | Pivoting and blocking |
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| 5 | Mon, | Feb 14 | Conditioning, error estimation, and refinement of linear systems |
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| Wed, | Feb 16 | Sparse, banded, and structured solves |
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| Fri, | Feb 18 | Other structured systems (Bindel away) |
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| 6 | Mon, | Feb 21 | Intro to least squares |
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| Wed, | Feb 23 | Least squares and QR |
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| Fri, | Feb 25 | Ill-posedness and regularization |
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| 7 | Mon, | Feb 28 | February break | |
| Wed, | Mar 02 | Ill-posedness and regularization |
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| Fri, | Mar 04 | Applications of eigenvalue problems |
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| 8 | Mon, | Mar 07 | Power iteration |
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| Wed, | Mar 09 | From power methods to QR iteration |
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| Fri, | Mar 11 | Hessenberg, tridiagonal, and bidiagonal |
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| 9 | Mon, | Mar 14 | Stationary iterations |
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| Wed, | Mar 16 | Gauss-Seidel convergence, extrapolation |
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| Fri, | Mar 18 | Krylov subspace iterations |
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| 10 | Mon, | Mar 21 | Nonlinear equations in 1D (Bindel away) |
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| Wed, | Mar 23 | Nonlinear equations in 1D (Bindel away) |
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| Fri, | Mar 25 | Optimization in 1D (Bindel away) |
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| 11 | Mon, | Mar 28 | Nonlinear equations and optimization |
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| Wed, | Mar 30 | Newton in many dimensions |
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| Fri, | Apr 01 | Gradient descent and Newton for optimization |
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| 12 | Mon, | Apr 04 | Spring break | |
| Wed, | Apr 06 | Spring break | ||
| Fri, | Apr 08 | Spring break | ||
| 13 | Mon, | Apr 11 | Gauss-Newton and nonlinear least squares |
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| Wed, | Apr 13 | Modified Newton iterations |
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| Fri, | Apr 15 | Quasi-Newton and other iterations |
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| 14 | Mon, | Apr 18 | Line search and globalization |
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| Wed, | Apr 20 | Trust regions |
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| Fri, | Apr 22 | Homotopy and continuation |
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| 15 | Mon, | Apr 25 | Constraints and multipliers |
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| Wed, | Apr 27 | Methods for equality constraints |
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| Fri, | Apr 29 | Methods for inequality constraints |
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| 16 | Mon, | May 02 | CANCELED (illness) |
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| Wed, | May 04 | Derivative free methods |
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| Fri, | May 06 | Review |
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| 17 | Mon, | May 09 | Review |
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