On computing multi-dimensional extreme eigen and singular subspaces

Author

Hasan, Mohammed A.

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Minnesota Duluth, Duluth, MN, USA

fYear

2010

fDate

May 30 2010-June 2 2010

Firstpage

2570

Lastpage

2573

Abstract

The problem, of finding extreme eigenvalues and eigenvectors of a real symmetric positive definite matrix can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach for computing higher dimensional sub-spaces corresponding to smallest and largest eigenvalues simultaneously. This approach is then generalized to develop dynamical system for computing the singular value spread of any real matrix.

Keywords

eigenvalues and eigenfunctions; optimisation; singular value decomposition; cost function approach; dynamical system; eigenvalues; eigenvectors; multidimensional extreme eigen subspaces; real symmetric positive definite matrix; singular subspaces; smooth optimization problem; Cost function; Eigenvalues and eigenfunctions; Equations; Iterative algorithms; Iterative methods; Manifolds; Neural networks; Principal component analysis; Symmetric matrices; Eigenvalue spread; Gradient dynamical systems; Joint PCA-MCA; Joint PSA-MSA; Oja´s Rule; Stiefel manifold;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems (ISCAS), Proceedings of 2010 IEEE International Symposium on

Conference_Location

Paris

Print_ISBN

978-1-4244-5308-5

Electronic_ISBN

978-1-4244-5309-2

Type

conf

DOI

10.1109/ISCAS.2010.5537100

Filename

5537100