A rational SHIRA method for the Hamiltonian eigenvalue problem Export

@article{RatSHIRA, abstract = {The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamiltonian eigenproblems by considering a suitable transformation. Structure induced shift-and-invert techniques are employed to steer the algorithm towards the interesting region of the spectrum. However, the shift cannot be altered in the middle of the computation without discarding the information that has been accumulated so far. This paper shows how SHIRA can be combined with ideas from Ruhe's Rational Krylov algorithm to yield a method that permits an adjustment of shift after every step of the computation, adding greatly to the flexibility of the algorithm. We call this new method rational SHIRA. A numerical example is presented to demonstrate its efficiency.}, author = {Benner, Peter and Effenberger, Cedric}, citeulike-article-id = {4431973}, citeulike-linkout-0 = {http://archiv.tu-chemnitz.de/pub/2009/0002/index.html}, day = {22}, institution = {TU Chemnitz, Fakult\"{a}t f\"{u}r Mathematik}, issn = {1864-0087}, journal = {Chemnitz Scientific Preprints, 08-08}, keywords = {arnoldi, eigenvalue, eigenwertproblem, hamiltonian, krylov, matrix, method, problem, rational, shift-and-invert, skew-hamiltonian, subspace}, month = {December}, posted-at = {2009-04-29 06:36:58}, priority = {2}, school = {TU Chemnitz, Fakult\"{a}t f\"{u}r Mathematik}, title = {A rational SHIRA method for the Hamiltonian eigenvalue problem}, url = {http://archiv.tu-chemnitz.de/pub/2009/0002/index.html}, year = {2008} }

TY - JOUR ID - RatSHIRA L3 - citeulike-article-id:4431973 N2 - The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamiltonian eigenproblems by considering a suitable transformation. Structure induced shift-and-invert techniques are employed to steer the algorithm towards the interesting region of the spectrum. However, the shift cannot be altered in the middle of the computation without discarding the information that has been accumulated so far. This paper shows how SHIRA can be combined with ideas from Ruhe's Rational Krylov algorithm to yield a method that permits an adjustment of shift after every step of the computation, adding greatly to the flexibility of the algorithm. We call this new method rational SHIRA. A numerical example is presented to demonstrate its efficiency. JF - Chemnitz Scientific Preprints, 08-08 SN - 1864-0087 TI - A rational SHIRA method for the Hamiltonian eigenvalue problem KW - arnoldi KW - eigenvalue KW - eigenwertproblem KW - hamiltonian KW - krylov KW - matrix KW - method KW - problem KW - rational KW - shift-and-invert KW - skew-hamiltonian KW - subspace AU - Benner, Peter AU - Effenberger, Cedric PY - 2008/12/22/ UR - http://archiv.tu-chemnitz.de/pub/2009/0002/index.html ER -