Tracking a few extreme singular values and vectors in signal processing
Article Abstract:
Computing large eigenvalues and associated eigenvectors is necessary for the approximation of a steadily changing covariance matrix in signal processing and other applications. The volume of computation involved in both the Eigenvalue Decomposition (EVD) and the Singular Value Decomposition (SVD) argues for the revision of this task in many situations, and several numerical techniques for performing the task are reviewed. Comparisons of the various techniques intended to ease the selection process are supported by computer simulations relevant to signal processing.
Publication Name: Proceedings of the IEEE
Subject: Electronics
ISSN: 0018-9219
Year: 1990
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Solving the generalized eigenvalue problem with singular forms
Article Abstract:
Two methods are developed for computing the generalized eiganvalues with singular forms. Conventional methods break down for the case of eigenvalues and eigenvectors associated with a matrix pair (A,B), where B is a singular Hermitian matrix, and A is not necessarily Hermitian, but has a range space which is a subset of the range space of B. An application is based on the ESPIRIT algorithm.
Publication Name: Proceedings of the IEEE
Subject: Electronics
ISSN: 0018-9219
Year: 1987
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Comments on 'solving the generalized eigenvalue problem with singular forms.' (comments)
Article Abstract:
The eigenvalue problem A times x equals lambda B times x where B is assumed to be a Hermitian matrix has been extensively studied by specialists in linear algebra. Most standard Fortran libraries include solutions for the case where the matrices A and B are real or complex. The QZ algorithm is the standard solution for the case in which A and B are both Hermitian.
Publication Name: Proceedings of the IEEE
Subject: Electronics
ISSN: 0018-9219
Year: 1989
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