Projects
Inverse-free rational Krylov methods: theory and applications KU Leuven
To keep the computational complexity of Krylov methods under control, one often switches to rational Krylov algorithms. Unfortunately rational Krylov methods still have quite some problems subjected to research in this project. We will investigate approximate rational Krylov algorithms, efficient data storage, and implicit restarts. We will test all our findings on realistic datasets stemming from applications.
Pole swapping methods for the eigenvalue problem - Rational QR algorithms KU Leuven
The matrix eigenvalue problem is often encountered in scientific computing
applications. Although it has an uncomplicated problem formulation, the best
numerical algorithms devised to solve it are far from obvious.
Computing all eigenvalues of a small to medium-sized matrix is nowadays a
routine task for an algorithm of implicit QR-type using a bulge chasing technique.
On the other hand projection methods are ...