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A Quasi-Newton Adaptive Algorithm for Estimating Generalized Eigenvectors

Mathew, G and Reddy, VU and Paulraj, A (1994) A Quasi-Newton Adaptive Algorithm for Estimating Generalized Eigenvectors. In: 1994 Conference Record of the Twenty-Eighth Asilomar Conference on Signals, Systems and Computers, 31st October-2nd November, Pacific Grove,CA, vol.1, 602 -606.


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We first introduce a constrained minimization formulation for the generalized symmetric eigenvalue problem and then recast it into an unconstrained minimization problem by constructing an appropriate cost function. The minimizer of this cost function corresponds to the eigenvector corresponding to the minimum eigenvalue of the given symmetric matrix pencil and all minimizers are global minimizers. We also present an inflation technique for obtaining multiple generalized eigenvectors of this pencil. Based on this asymptotic formulation, we derive a quasi-Newton adaptive algorithm for estimating these eigenvectors in the data case. This algorithm is highly modular and parallel with a computational complexity of $O(N_2)$multiplications, N being the problem-size. Simulation results show fast convergence and good quality of the estimated eigenvectors.

Item Type: Conference Paper
Publisher: IEEE
Additional Information: Copyright 1994 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 25 Aug 2008
Last Modified: 19 Sep 2010 04:28
URI: http://eprints.iisc.ac.in/id/eprint/7281

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