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Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method

By Peter Benner, Heike Fassbender and Martin Stoll


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 propose several shift-and-invert operators with Hamiltonian structure. Our approach is tested for several examples from structural analysis and gyroscopic systems

Topics: Numerical analysis
Publisher: Unspecified
Year: 2007
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