NDLI: RLS-based adaptive algorithms for generalized eigen-decomposition

Content Provider	IEEE Xplore Digital Library
Author	Jian Yang Hongsheng Xi Feng Yang Yu Zhao
Copyright Year	1991
Abstract	The aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen-decomposition problem which arises in a variety of modern signal processing applications. First, we reinterpret the generalized eigen-decomposition problem as an unconstrained minimization problem by constructing a novel cost function. Second, by applying projection approximation method and recursive least-square (RLS) technique to the cost function, a parallel adaptive algorithm for a basis for the r-dimensional (r>0) dominant generalized eigen-subspace and a sequential algorithm based on deflation technique for the first r-dominant generalized eigenvectors are derived. These algorithms can be viewed as counterparts of the extended projection approximation subspace tracking (PAST) and PASTd algorithms, respectively. Furthermore, we modify the parallel algorithm to explicitly estimate the first r-generalized eigenvectors in parallel, not the generalized eigen-subspace. More important, the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences, while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique. Third, following convergence analysis methods for PAST and PASTd, we prove the asymptotic convergence properties of the proposed algorithms. Finally, computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms.
Sponsorship	IEEE Signal Processing Society
Starting Page	1177
Ending Page	1188
Page Count	12
File Size	517472
File Format	PDF
ISSN	1053587X
Volume Number	54
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Adaptive algorithm Signal processing algorithms Approximation algorithms Convergence Cost function Parallel algorithms Adaptive signal processing Approximation methods Resonance light scattering Computer errors recursive least-square (RLS) Adaptive algorithms generalized eigen-decomposition generalized eigenvector matrix pencil
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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