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 20 Lecture 1 - Introduction (syllabus)
Week 1-1, Aug 22 Lecture 2 - What a matrix is and three fundamental problems: linear systems, least squares, eigenvalues.
Week 2-1, Aug 27 Lecture 3 - Matrix structure: Hankel, Toeplitz, and Sparsity
Week 2-2, Aug 29 Lecture 4 - Matrix structure: SPD, Orthogonal, M-matrix, Triangular, Hessenberg
Week 3-1, Sep 3 Lecture 5 - Sparse matrix storage, Norms
HW HW1 Due September 6th. (Covers Unit 1)

Unit 2 - Simple algorithms

Week 3-2, Sep 5 Lecture 6 - Neumann series and Richardson's method
Week 4-1, Sep 10 Lecture 7 - Minimizers of Quadratic functions and linear systems
Week 4-2, Sep 12 Lecture 8 - Steepest descent and coordinate descent
Week 5-1, Sep 17 Lecture 9 - Jacobi and Gauss Seidel
Week 5-2, Sep 19 Lecture 10 - The power method
HW HW2 Due September 20. (Covers Unit 2)

Unit 3 - Finitely terminating algorithms

Week 6-1, Sep 24 - 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 26 - Lecture 12.
HW HW3a Due Sept 27. (Covers start of Unit 3 for exam, this will likely be optional.)
Week 7-1, Oct 1 - Lecture 13 - QR factorization and Exam prep.

EXAM 1

Week 7-2, Oct 2 - EXAM Evening exam. "Lecture 14" Covers units 1, 2, and LU (but not QR).

Unit 3 - Finitely terminating algorithms continued.

Week 8-1, Oct 8 Fall break.
Week 8-2, Oct 10 Lecture 15 - Householder QR, FLOP counts
HW HW3b Conceptually due Oct 18.

Unit 4 - Conditioning and Stability

Week 9-1, Oct 15 Lecture 16 - The condition number of a problem
Week 9-2, Oct 17 Lecture 17 - The matrix condition number as a fundamental quantity
Week 10-1, Oct 22 Lecture 18 - Floating point formats and bad variance computations
Week 10-2, Oct 24 Lecture 19 - Error analysis and (long) error analysis of LU
HW HW4 Due Nov 1.

Unit 5 - Advanced problems

Week 11-1, Oct 29 Lecture 20 - Beyond the three fundamental problems. Sequences of linear systems, generalized eigenvalues, functions of a matrix
Week 11-2, Oct 31 Lecture 21 - Matrix functions (and intro to Krylov methods, Unit 6)
HW HW5 Due November 15 (Covers Unit 5)

Unit 6 - Krylov methods

Week 12-1, Nov 5 Lecture 22 - Simple Krylov subspaces and the Arnoldi process
Week 12-2, Nov 7 Lecture 23 - The Lanczos process for symmetric matrices
Week 13-1, Nov 12 Lecture 24 - The Conjugate Gradient method based on Lanczos
Week 13-2, Nov 14 Lecture 25 - The GMRES method and CG via orthogonal polynomials
Week 14-1, Nov 19 Lecture 26 - Preconditioners
HW HW6 Due Dec 1 (Covers Unit 6)

Unit 7 - Eigenvalue algorithms.

Week 14-2, Nov 21 Lecture 27 - Block power method, subspace iteration, QR method intro
Week 15-1, Nov 26 Lecture 28 - QR and Subspace Iteration and Tridiagonal reduction
Week 15-2, Nov 28 Thanksgiving break
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.

Matrix Computations

David Gleich

Purdue University

Fall 2024

Course number CS-51500

Tuesday-Thursday 10:30-11:45pm.