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

CITATIONS