Computation of matrix eigenvalues forms one of the basic problems in numerical linear algebra and is of fundamental importance in applied science and engineering. In this paper, "Trace Inverse Algorithms" in rational and radical forms are introduced. These algorithms are applied for computing the eigenvalues of rank one modification, bordered matrices, and the Hessenberg eigenvalue problem. Using this approach a sample of extremum eigenvalue finders are developed. These methods are iterative and can be designed to have convergence of any prescribed order. Generalization to the general nonlinear eigenvalue problem is also presented.
|Original language||English (US)|
|Number of pages||6|
|Journal||Proceedings of the IEEE Conference on Decision and Control|
|State||Published - Dec 1 2002|
|Event||41st IEEE Conference on Decision and Control - Las Vegas, NV, United States|
Duration: Dec 10 2002 → Dec 13 2002