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).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {29},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a0/}
}
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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/