Title :
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
fDate :
May 30 2010-June 2 2010
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;
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
DOI :
10.1109/ISCAS.2010.5537100
