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A Numerical Method for Computing an SVD-like Decomposition
Xu, Hongguo
Xu, Hongguo
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Abstract
We present a numerical method for computing the SVD-like decomposition B = QDS-1 , where Q is orthogonal, S is symplectic, and D is a permuted diagonal matrix. The method can be applied directly to compute the canonical form of the Hamiltonian matrices of the form JBTB , where $J=[{0 \atop -I}{I \atop 0}]$. It can also be applied to solve the related application problems such as the gyroscopic systems and linear Hamiltonian systems. Error analysis and numerical examples show that the eigenvalues of JBTB computed by this method are more accurate than those computed by the methods working on the explicit product JBTB or BJBT .
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This is the published version, also available here: http://dx.doi.org/10.1137/S0895479802410529.
Date
2005-09-05
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Society for Industrial and Applied Mathematics
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Keywords
skew-symmetric matrix, QR algorithm, Jacobi algorithm, Hamitonian matrix, symplectic matrix, orthogonal symplectic, eigenvalue problem, SVD, SVD-like decomposition, Schur form, Jordan canonical form
Citation
Xu, Hongguo. "A Numerical Method for Computing an SVD-like Decomposition." (2005) SIAM. J. Matrix Anal. & Appl., 26(4), 1058–1082. (25 pages). http://dx.doi.org/10.1137/S0895479802410529.