A new algorithm for the generalized eigenvalue problem

Author

Hüper, Knut ; Helmke, Uwe

Author_Institution

Dept. of Math., Wurzburg Univ., Germany

Volume

1

fYear

1997

fDate

21-24 Apr 1997

Firstpage

35

Abstract

The problem of finding the generalized eigenvalues and eigenvectors of a pair of real symmetric matrices A and B, with B>0, can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach to the generalized eigenvalue problem which is posed on the product of the n-sphere and Euclidian space R . The critical point set of this cost function is studied. An algorithm is presented based on constrained optimization. A proof of local quadratic convergence is given

Keywords

convergence of numerical methods; eigenvalues and eigenfunctions; matrix algebra; optimisation; signal processing; Euclidian space; constrained optimization; cost function; generalized eigenvalue problem; generalized eigenvectors; local quadratic convergence; n-sphere; orthogonal Jacobi-type transformations; real symmetric matrices; signal procesing algorithm; smooth manifold; smooth optimization problem; Constraint optimization; Convergence; Cost function; Eigenvalues and eigenfunctions; Jacobian matrices; Mathematics;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on

Conference_Location

Munich

ISSN

1520-6149

Print_ISBN

0-8186-7919-0

Type

conf

DOI

10.1109/ICASSP.1997.598866

Filename

598866