Robust eigenvalue solvers
Researchers
Description
This research has been discontinued.
In this department, a large effort was done in understanding and developing robust numerical methods for the calculation of the rightmost eigenvalue of large sparse matrices. The QR-method is no more feasible due to execution time and computer memory limitations. Research was concentrated on the issue of implicitly restarting iterative eigenvalue algorithm, especially the Rational Krylov Sequence method and the unsymmetric Lanczos algorithm. Both methods build Krylov type subspaces in which the eigenvalue problem is approximated. If the size of the subspace becomes too large, then a restarting algorithm reduces it to a smaller, but equally efficient, subspace. The restarting procedure implicitly implies a rational or polynomial filter function on the resulting subspace. This filter can be used for the removal of spurious information in the set of approximation values. Analogously, the possibility of implicitly restarting and implicitly filtering inexact eigenvalue solvers is studied. An inexact solver is an algorithm that allows the use of inaccurate linear system solutions within its iteration steps.
This research is discontinued since 1998.
PhD Thesis: Gorik Desamblanx: Filtering and Restarting Projection Methods for Eigenvalue Problems (June 2, 1998)
