Abstract
Many algorithms exist for computing the symmetric and nonsymmetric eigendecomposition. In this paper, we present several new algorithms and improvements for solving the general symmetric and nonsymmetric nonlinear eigenvalue problem. These methods include "Trace Inverse Algorithms" in rational and radical forms. They also include a line search method for computing eigenpairs. We first discuss variations of the Newton method for finding eigenvalues and eigenvectors from which a trace inverse algorithm is developed. We then discuss a Krylov method for medium and large size problems. Additionally, methods for computing minimum and maximum eigenpairs are proposed. Using this approach, a sample of extremum eigenvalue finders are presented.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1470-1475 |
| Number of pages | 6 |
| Journal | Proceedings of the American Control Conference |
| Volume | 2 |
| State | Published - 2003 |
| Event | 2003 American Control Conference - Denver, CO, United States Duration: Jun 4 2003 → Jun 6 2003 |