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Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (1994)
Pacific Grove, CA, USA
Oct. 31, 1994 to Nov. 2, 1994
ISSN: 1058-6393
ISBN: 0-8186-6405-3
pp: 602-606
G. Mathew , Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India
V.U. Reddy , Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India
A. Paulraj , Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India
ABSTRACT
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 /spl Oscr/(N/sup 2/) multiplications, N being the problem-size. Simulation results show fast convergence and good quality of the estimated eigenvectors.<>
INDEX TERMS
adaptive signal processing, Newton method, minimisation, eigenvalues and eigenfunctions, convergence of numerical methods, matrix algebra, estimation theory, computational complexity
CITATION

G. Mathew, V. Reddy and A. Paulraj, "A quasi-Newton adaptive algorithm for estimating generalized eigenvectors," Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers(ACSSC), Pacific Grove, CA, USA, 1995, pp. 602-606.
doi:10.1109/ACSSC.1994.471523
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