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Some remarks on the complex J-symmetric eigenproblem / Peter Benner, Heike Faßbender, Chao Yang
VerfasserBenner, Peter ; Faßbender, Heike ; Yang, Chao
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, July, 2015
Umfang1 Online-Ressource (20 Seiten = 0,1 MB)
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 15-12
URNurn:nbn:de:gbv:3:2-64788 
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Some remarks on the complex J-symmetric eigenproblem [0.31 mb]
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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.