Algorithms for the Generalized and Nonlinear Eigenvalue Problems

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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 languageEnglish (US)
Pages (from-to)1470-1475
Number of pages6
JournalProceedings of the American Control Conference
Volume2
StatePublished - Nov 7 2003
Event2003 American Control Conference - Denver, CO, United States
Duration: Jun 4 2003Jun 6 2003

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