Geodesic
Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method
Electronic transactions on numerical analysis, Tome 29 (2008)
We consider the numerical solution of quadratic eigenproblems with spectra that exhibit Hamiltonian symmetry. We propose to solve such problems by applying a Krylov-Schur-type method based on the symplectic Lanczos process to a structured linearization of the quadratic matrix polynomial. In order to compute interior eigenvalues, we discuss several shift-and-invert operators with Hamiltonian structure. Our approach is tested for several examples from structural analysis and gyroscopic systems.
Classification : 65F15, 15A24, 47A75, 47H60
Keywords: quadratic eigenvalue problem, Hamiltonian symmetry, Krylov subspace method, symplectic Lanczos process, gyroscopic systems 
@article{ETNA_2008__29__a0,
     author = {Benner,  Peter and Fassbender,  Heike and Stoll,  Martin},
     title = {Solving large-scale quadratic eigenvalue problems with {Hamiltonian} eigenstructure using a structure-preserving {Krylov} subspace method},
     journal = {Electronic transactions on numerical analysis},
     year = {2008},
     volume = {29},
     zbl = {1171.65374},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a0/}
}
TY  - JOUR
AU  - Benner,  Peter
AU  - Fassbender,  Heike
AU  - Stoll,  Martin
TI  - Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method
JO  - Electronic transactions on numerical analysis
PY  - 2008
VL  - 29
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__29__a0/
LA  - en
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%0 Journal Article
%A Benner,  Peter
%A Fassbender,  Heike
%A Stoll,  Martin
%T Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method
%J Electronic transactions on numerical analysis
%D 2008
%V 29
%U http://geodesic.mathdoc.fr/item/ETNA_2008__29__a0/
%G en
%F ETNA_2008__29__a0
Benner,  Peter; Fassbender,  Heike; Stoll,  Martin. Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method. Electronic transactions on numerical analysis, Tome 29 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__29__a0/