An implicit Jacobi-like method for computing generalized hyperbolic SVD

In this paper, we introduce a joint hyperbolic-orthogonal decomposition of two matrices which we call a generalized hyperbolic singular value decomposition, or GHSVD. This decomposition can be used for finding the eigenvalues and eigenvectors of a symmetric definite pencil X T X−λY T ΦY where Φ= dia...

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Bibliographic Details
Published in:Linear algebra and its applications 2003, Vol.358 (1), p.293-307
Main Author: Bojanczyk, Adam W.
Format: Article
Language:English
Subjects:
Hyperbolic singular value decomposition
Hyperbolic transformations
Jacobi method
Symmetric definite pencil
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Summary:In this paper, we introduce a joint hyperbolic-orthogonal decomposition of two matrices which we call a generalized hyperbolic singular value decomposition, or GHSVD. This decomposition can be used for finding the eigenvalues and eigenvectors of a symmetric definite pencil X T X−λY T ΦY where Φ= diag(±1) . We also present an implicit Jacobi-like method for computing this GHSVD.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(02)00394-4