As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.
| Date | Class Topic | Reading (Watkins) |
|---|---|---|
| 1/17 | Course introduction, how systems of linear equations arise in applications | 1.1-1.2 |
| 1/19 | Linear equations in tomography | (notes) |
| 1/22 | Getting started with MATLAB | 1.1-1.2 |
| 1/24 | Computer arithmetic and round-off error | |
| 1/26 | More on computer arithmetic and round-off | |
| 1/29 | Triangular systems, Cholesky factorization | 1.3 |
| 1/31 | Computing Cholesky factorization | 1.4 |
| 2/2 | ``Banded'' and sparse examples | 1.5-1.6 |
| 2/5 | Gauss elimination and A = LU factorization | 1.7 |
| 2/7 | GE with row interchanges and pivoting | 1.8 |
| 2/9 | Vector and matrix norms | 2.1 |
| 2/12 | Condition numbers | 2.2 |
| 2/14 | Error analysis | 2.3 - 2.5 |
| 2/16 | More on error analysis | 2.3 - 2.5 |
| 2/19 | Overdetermined systems and least squares | 3.1 |
| 2/21 | Orthogonal matrices | 3.2 |
| 2/23 | Reflection and rotation matrices | 3.2 |
| 2/26 | QR factorization | 3.2 |
| 2/28 | The QR algorithm | 3.2 |
| 3/2 | More on the QR algorithm | 3.2 |
| 3/5,7,9 | No Class -- Spring Break | 3.3-3.5 |
| 3/12 | QR and least squares | 3.3 |
| 3/14 | Geometry of QR | 3.4-3.5 |
| 3/16 | Spare Day | 3.5 |
| 3/19 | The singular value decomposition (SVD) | 4.1 |
| 3/21 | Applications of SVD | 4.2 |
| 3/23 | SVD and least squares | 4.3 |
| 3/26 | Eigenvalues and eigenvectors | 5.1-5.2 |
| 3/28 | Power method and extensions | 5.3 |
| 3/30 | Shifted power methods | 5.3 |
| 4/2 | Symmetric eigenvalue problems and QR | 5.4 |
| 4/4 | More on the symmetric eigenvalue problem | 5.4 |
| 4/6,9 | No Class -- Easter Break | 5.5 |
| 4/11 | Iterative methods for linear systems (Jacobi) | 7.1 |
| 4/13 | Gauss-Seidel and generalizations | 7.2 |
| 4/16 | Analyzing rates of convergence | |
| 4/18 | Spectral radius and Gershgorin's theorem | |
| 4/20 | Landweber iteration | (notes) |
| 4/23 | Applications in tomography | |
| 4/25 | Applications in tomography | |
| 4/27 | Applications in tomography | |
| 4/30 | Course wrap-up |
Last modified: January 10, 2007