This is a graduate course in numerical linear algebra, assuming familiarity with undergraduate linear algebra and basic programming skills. We will be studying fundamental ideas such as the singular value decomposition, factorizations for least squares and linear systenms, eigenvalues, and iterative methods.
| Instructor | Robert Kirby (kirby.at.uchicago.edu) |
| Time | MWF 11:30-12:20 |
| Place | Ryerson 277 (in the annex) |
| Office hours | MWF 10:30-11:20//Ryerson 259 |
There will be weekly homework assignments, plus a midterm and a final exam. Each will be weighted as a third of the grade.
Our main text is "Numerical Linear Algebra" by Trefethen and Bau (SIAM press). You may order it online from SIAM or Amazon.com. SIAM gives notoriously bad deals to university book stores, so it is not available on campus.
Another good book is "Applied Numerical Linear Algebra" by Demmel, also from SIAM press
An encyclopedic reference is "Matrix Computations" by Golub & van Loan.
| Date | Material |
| 26 Sept 05 | Class information, Matrices, vectors, inner products, and orthogonality |
| 28 Sept 05 | Orthogonality and norms |
| 30 Sept 05 | The singular value decomposition |
| 3 Oct 05 | More on the SVD |
| 5 Oct 05 | Projections |
| 7 Oct 05 | The QR factorization & Gram Schmidt |
| 10 Oct 05 | Householder triangularization |
| 12 Oct 05 | Least squares problems |
| 14 Oct 05 | Conditioning of mathematical problems |
| 17 Oct 05 | Floating point arithmetic, stability |
| 19 Oct 05 | More on stability |
| 21 Oct 05 | Stability, cont'd |
| 24 Oct 05 | Conditioning of least squares |
| 26 Oct 05 | Stability for least squares |
| 28 Oct 05 | Rank-deficient least squares |
| 31 Oct 05 | LU factorization |
| 2 Nov 05 | Stability of LU factorization and pivoting |
| 4 Nov 05 | Midterm |
| 7 Nov 05 | Eigenvalue problems |
| 9 Nov 05 | Basic pieces of eigenvalue solvers |
| 11 Nov 05 | Iteration schemes |
| 14 Nov 05 | QR Algorithm and shifting |
| 16 Nov 05 | Computing the SVD |
| 18 Nov 05 | Introducing iterative methods |
| 21 Nov 05 | Arnoldi iteration |
| 23 Nov 05 | No class |
| 25 Nov 05 | No class |
| 28 Nov 05 | GMRES |
| 30 Nov 05 | Conjugate Gradients |
| 2 Dec 05 | Preconditioning |
Problem numbers refer to Exercises in Trefethen and Bau.
| Due Date | Problems |
| 3 Oct 2005 | 1.1,1.2,2.5,2.6,3.2,3.6,4.1,4.3,4.4 |
| 10 Oct 2005 | 5.2,5.4,6.1,6.2,6.3,6.5,7.2,7.4,7.5 |
| 17 Oct 2005 | 8.2,8.3,10.1,10.2,10.3,11.1,11.2,12.2,12.3 |
| 24 Oct 2005 | 13.2,13.3,14.1,15.1,16.2,17.2 |
| 31 Oct 2005 | 18.1,18.4,19.1,20.1 |
| 14 Nov 2005 | 20.2,20.3,21.2,21.6,24.2,25.2,26.3 |
| 21 Nov 2005 | 27.3,27.4,28.2,29.1 |
| 2 Dec 2005 | 31.3,33.2,35.4,38.3 |
Work the following problems from Trefethen and Bau. You may use the textbook, Demmel, Golub and van Loan, or course notes. You may not refer to material found on the Internet. You may use MATLAB/Octave. You may not consult with any other person or people while working the exam. 9.2, 10.4, 16.1, 25.3, 27.1, 35.6. Solutions are due Monday, December 5, 2005 at noon, at the instructor's office.