We consider large and sparse eigenproblems where the spectrum exhibits
special symmetries. Here we focus on Hamiltonian symmetry, that is,
the spectrum is symmetric with respect to the real and imaginary
axes. After briefly discussing quadratic eigenproblems with
Hamiltonian spectra we review structured Krylov subspace methods to
aprroximate parts of the spectrum of Hamiltonian operators. We will
discuss the optimization of the free parameters in the resulting
symplectic Lanczos process in order to minimize the conditioning of
the (non-orthonormal) Lanczos basis. The effects of our findings are
demonstrated for several numerical examples.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-201000852 |
| Date | 12 June 2010 |
| Creators | Benner, Peter |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:lecture |
| Format | application/pdf, text/plain, application/zip |
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