Some remarks on the complex J-symmetric eigenproblem / Peter Benner, Heike Faßbender, Chao Yang
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870919083
URN
urn:nbn:de:gbv:3:2-64788
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Erschienen
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, July, 2015
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1 Online-Ressource (20 Seiten = 0,1 MB)
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Sprache
eng
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Inhaltliche Zusammenfassung
Abstract: The eigenproblem for complex J-symmetric matrices is considered. A proof of the existence of a transformation to the complex J-symmetric Schur form proposed in [C. Mehl. On asymptotic convergence of nonsymmetric Jacobi algorithms. SIAM J. Matrix Anal. Appl., 30:291-311, 2008.] is given. The complex symplectic unitary QR decomposition and the complex symplectic SR decomposition are discussed. It is shown that a QR-like method based on the complex symplectic unitary QR decomposition is not feasible here. A complex symplectic SR algorithm is presented which can be implemented such that one step of the SR algorithm can be carried out in O(n) arithmetic operations. Based on this, a complex symplectic Lanczos method can be derived. Moreover, it is discussed how the 2n x 2n complex J-symmetric matrix can be embedded in a 4n x 4n real Hamiltonian matrix.
Schriftenreihe
Max Planck Institute Magdeburg Preprints ; 15-12 ppn:870173030