A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

Mathew, George and Reddy, VU (1996) A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem. In: IEEE Transactions On Signal Processing, 44 (10). pp. 2413-2422.

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Abstract

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Item Type:	Journal Article
Publication:	IEEE Transactions On Signal Processing
Publisher:	IEEE
Additional Information:	Copyright 1996 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:	03 Dec 2009 11:36
Last Modified:	19 Sep 2010 05:28
URI:	http://eprints.iisc.ac.in/id/eprint/19388

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