Title :
A new algorithm for the generalized eigenvalue problem
Author :
Hüper, Knut ; Helmke, Uwe
Author_Institution :
Dept. of Math., Wurzburg Univ., Germany
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;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on
Conference_Location :
Munich
Print_ISBN :
0-8186-7919-0
DOI :
10.1109/ICASSP.1997.598866
