Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods

Authors:
Tsung-Min Hwang;Wen-Wei Lin;Volker Mehrmann
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2002

Citing 0
Cited 4

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Quadratic inverse eigenvalue problem for damped gyroscopic systems

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Abstract

Numerical methods for the solution of large scale structured quadratic eigenvalue problems are discussed. We describe a new extraction procedure for the computation of eigenvectors and invariant subspaces of skew-Hamiltonian/Hamiltonian pencils using the recently proposed skew-Hamiltonian isotropic implicitly restarted Arnoldi method (SHIRA).As an application we discuss damped gyroscopic systems. For this problem we first solve the eigenvalue problem for the undamped system using the structure-preserving method and then use the quadratic Jacobi--Davidson method as correction procedure. We also illustrate the properties of the new approach for several other application problems.