| Lab Number | Title | Date | Links |
|---|---|---|---|
| 1 | Solving the Least Squares Problem | 1/29 | |
| 2 | Sensitivity of the Least Squares Problem | 2/12 | |
| 3 | Rayleigh Quotient Iteration | 2/26 | |
| 4 | Francis's Algorithm | 3/12 | |
| 5 | Eigenvalue and SVD Computations | 3/19 | |
| 6 | Applications of Eigenvalues I | 4/2 | |
| 7 | Applications of Eigenvalues II | 4/14 | |
| 8 | Applications of Eigenvalues III | 4/23 |
In this course, we will discuss one of the most important algorithms of the 20th century: Francis's Implicitly Shifted QR Algorithm. This algorithm changed the eigenvalue problem from difficult to routine in the early 1960s. It was later ranked as one of the top ten algorithms of the 20th century by Jack Dongarra and Francis Sullivan in the January/February 2000 issue of Computing in Science and Engineering. Armed with a reliable eigenvalue solver, we will be able to tackle other problems such as the singular value decomposition, least squares problem, and systems of differential equations. Applications include, but are not limited to, linear regression, roots of polynomials, principal component analysis, page rank, and graph clustering.
