A Large, Sparse, and Indefinite Generalized Eigenvalue Problem from Fluid Mechanics

A numerical method for calculating the minimum positive eigenvalue of a sparse, indefinite, Hermitian algebraic problem has been developed. The method is based on inverse iteration and is a generalization of a procedure previously employed for the simpler problem of finding the smallest eigenvalue o...

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Bibliographic Details
Published in:SIAM journal on scientific and statistical computing 1992-01, Vol.13 (1), p.411-424
Main Authors: Mittelmann, Hans D., Law, Cindy C., Jankowski, Daniel F., Neitzel, G. Paul
Format: Article
Language:English
Subjects:
Algorithms
Eigenvalues
Energy
Fluid mechanics
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Summary:A numerical method for calculating the minimum positive eigenvalue of a sparse, indefinite, Hermitian algebraic problem has been developed. The method is based on inverse iteration and is a generalization of a procedure previously employed for the simpler problem of finding the smallest eigenvalue of a positive-definite matrix. Motivation was provided by a three-dimensional research problem from hydrodynamic stability. Stability limits obtained from the application of the method to a previously studied problem are compared to independently determined results.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0913022