Course schedule
The overall course breaks down into 7 units.
Please see the readings page for an up to date
list of course materials.
Lecture numbers are based on 2019 videos.
Homework dates are approximately correct and mainly for guidance.
I reserve the right to adjust them slightly. (In particular, I often give you the weekend as
an automatic extension.) Note that homework 3 is split into two parts corresponding to
around the midterm.
Unit 1 - Getting started: Notation, Matrix Structure, Sparsity
- Week 1-1, Aug 22 Lecture 1 - Introduction (syllabus)
- Week 1-1, Aug 24 Lecture 2 - What a matrix is and three fundamental problems: linear systems, least squares, eigenvalues.
- Week 2-1, Aug 29 Lecture 3 - Matrix structure: Hankel, Toeplitz, and Sparsity
- Week 2-2, Sep 31 Lecture 4 - Matrix structure: SPD, Orthogonal, M-matrix, Triangular, Hessenberg
- Week 3-1, Sep 5 Lecture 5 - Sparse matrix storage, Norms
- HW HW1 Due September 8th. (Covers Unit 1)
Unit 2 - Simple algorithms
- Week 3-2, Sep 7 Lecture 6 - Neumann series and Richardson's method
- Week 4-1, Sep 12 Lecture 7 - Minimizers of Quadratic functions and linear systems
- Week 4-2, Sep 14 Lecture 8 - Steepest descent and coordinate descent
- Week 5-1, Sep 19 Lecture 9 - Jacobi and Gauss Seidel
- Week 5-2, Sep 21 Lecture 10 - The power method
- HW HW2 Due September 22. (Covers Unit 2)
Unit 3 - Finitely terminating algorithms
- Week 6-1, Sep 26 - Lecture 11, 12 Double header, Variable Elimination and LU, Pivoting and Variable Elimination (lots to watch here, but it's all very related.)
- Week 6-2, Sep 28 - Lecture 12.
- HW HW3a Due Sept 29. (Covers start of Unit 3 for exam, this will likely be optional.)
- Week 7-1, Oct 3 - Lecture 13 - QR factorization and Exam prep.
EXAM 1
- Week 7-2, Oct 5 - EXAM Evening exam. "Lecture 14" Covers units 1, 2, and LU (but not QR).
Unit 3 - Finitely terminating algorithms continued.
- Week 8-1, Oct 10 Fall break.
- Week 8-2, Oct 12 Lecture 15 - Householder QR, FLOP counts
- HW HW3b Conceptually due Oct 20.
Unit 4 - Conditioning and Stability
- Week 9-1, Oct 17 Lecture 16 - The condition number of a problem
- Week 9-2, Oct 19 Lecture 17 - The matrix condition number as a fundamental quantity
- Week 10-1, Oct 24 Lecture 18 - Floating point formats and bad variance computations
- Week 10-2, Oct 26 Lecture 19 - Error analysis and (long) error analysis of LU
- HW HW4 Due Nov 3.
Unit 5 - Advanced problems
- Week 11-1, Oct 31 Lecture 20 - Beyond the three fundamental problems. Sequences of linear systems, generalized eigenvalues, functions of a matrix
- Week 11-2, Nov 2 Lecture 21 - Matrix functions (and intro to Krylov methods, Unit 6)
- HW HW5 Due November 17 (Covers Unit 5)
Unit 6 - Krylov methods
- Week 12-1, Nov 7 Lecture 22 - Simple Krylov subspaces and the Arnoldi process
- Week 12-2, Nov 9 Lecture 23 - The Lanczos process for symmetric matrices
- Week 13-1, Nov 14 Lecture 24 - The Conjugate Gradient method based on Lanczos
- Week 13-2, Nov 16 Lecture 25 - The GMRES method and CG via orthogonal polynomials
- Week 14-1, Nov 21 Lecture 26 - Preconditioners
- Week 14-2, Nov 23 Thanksgiving break
- HW HW6 Due Dec 1 (Covers Unit 6)
Unit 7 - Eigenvalue algorithms.
- Week 15-1, Nov 28 Lecture 27 - Block power method, subspace iteration, QR method intro
- Week 15-2, Nov 30 Lecture 28 - QR and Subspace Iteration and Tridiagonal reduction
- Week 16-1, Dec 5 Lecture 29 - The SVD and Bipartite Matrices (or Property A)
- Week 16-2, Dec 7 Lecture 30 - Randomized methods
- HW Probably optional.
FINAL EXAM
- Covers all class, but focused on units 3-7.