Schedule

This schedule should be considered tentative and subject to change, at least until it actually takes place!

In addition to the course notes, I have posted some background notes. Some material in these notes is truly background that you will have seen in prior classes. Other material may be new to you, and some of it will be covered in class. You should feel free to ask questions about any of this!

Week Day Date Notes and readings HW
Fri, Aug 30 Introduction and matrix multiply
1 Mon, Sep 02 Labor Day
Wed, Sep 04 Structured matrix multiply
Fri, Sep 06 Some linear algebra review
2 Mon, Sep 09 Matrix calculus
Wed, Sep 11 Sensitivity and conditioning
Fri, Sep 13 Floating point and error analysis basics
3 Mon, Sep 16 Building blocks for error analysis
Wed, Sep 18 Introduction to Gaussian elimination
Fri, Sep 20 Schur complements, blocking, and pivoting
4 Mon, Sep 23 Backward error, iterative refinement
Wed, Sep 25 Condition estimation, scaling, symmetric matrices
Fri, Sep 27 Structured linear systems
5 Mon, Sep 30 Matrices and graphs; nested dissection
Wed, Oct 02 Introduction to least squares
Fri, Oct 04 Householder, Givens, and QR
6 Mon, Oct 07 Constraints, sparsity, projections
Wed, Oct 09 Sensitivity of least squares
Fri, Oct 11 Rank-deficiency and regularization
7 Mon, Oct 14 Indigenous People's Day
Wed, Oct 16 Regularization choices; matrix nearness problems
Fri, Oct 18 Kernels and least squares
8 Mon, Oct 21 Introduction to eigenvalue problems
Wed, Oct 23 Perturbation theory
Fri, Oct 25 Power iterations
9 Mon, Oct 28 Subspace iterations and QR
Wed, Oct 30 Hessenberg QR
Fri, Nov 01 Theory for symmetric eigenproblems and SVD
10 Mon, Nov 04 Theory for symmetric eigenproblems and SVD
Wed, Nov 06 Solver ideas for SEP and SVD
Fri, Nov 08 Other eigenvalue problems
11 Mon, Nov 11 Veterans Day
Wed, Nov 13 Model problems for iterative methods
Fri, Nov 15 Splittings, sweeps, and stationary iterations
12 Mon, Nov 18 Approximation from subspaces
Wed, Nov 20 Krylov subspaces
Fri, Nov 22 Lanczos and Arnoldi
13 Mon, Nov 25 Conjugate gradients
Wed, Nov 27 Thanksgiving break
Fri, Nov 29 Thanksgiving break
14 Mon, Dec 02 Snow day
Wed, Dec 04 Other Krylov subspace methods
Fri, Dec 06 Krylov subspace methods for eigenproblems
15 Mon, Dec 09 Review