Computing extreme subspaces using Mirsky theorem

Mohammed A. Hasan

doi:10.1109/ISCAS.2009.5118350

Computing extreme subspaces using Mirsky theorem

Mohammed A. Hasan

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Extreme eigenpairs computation is of considerable interest in signal processing and estimation. Thus problem of simultaneous computation of the smallest and largest eigenvalues and the corresponding eigenvectors of a symmetric matrix is considered. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Dynamical systems that converge to extreme eigenvectors are derived from necessary optimality conditions which are given in terms of a gradient of certain cost functions over a Stiefel manifold. Numerical examples are given to examine the convergence.

Original language	English (US)
Title of host publication	2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
Pages	2665-2668
Number of pages	4
DOIs	https://doi.org/10.1109/ISCAS.2009.5118350
State	Published - 2009
Event	2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009 - Taipei, Taiwan, Province of China Duration: May 24 2009 → May 27 2009

Publication series

Name	Proceedings - IEEE International Symposium on Circuits and Systems
ISSN (Print)	0271-4310

Other

Other	2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
Country/Territory	Taiwan, Province of China
City	Taipei
Period	5/24/09 → 5/27/09

Keywords

Eigenvalue spread
Gradient dynamical systems; Stiefel manifold
Joint PCA-MCA
Joint PSA-MSA
Oja's rule

Publisher link

10.1109/ISCAS.2009.5118350

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Hasan, MA 2009, Computing extreme subspaces using Mirsky theorem. in 2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009., 5118350, Proceedings - IEEE International Symposium on Circuits and Systems, pp. 2665-2668, 2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009, Taipei, Taiwan, Province of China, 5/24/09. https://doi.org/10.1109/ISCAS.2009.5118350

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abstract = "Extreme eigenpairs computation is of considerable interest in signal processing and estimation. Thus problem of simultaneous computation of the smallest and largest eigenvalues and the corresponding eigenvectors of a symmetric matrix is considered. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Dynamical systems that converge to extreme eigenvectors are derived from necessary optimality conditions which are given in terms of a gradient of certain cost functions over a Stiefel manifold. Numerical examples are given to examine the convergence.",

keywords = "Eigenvalue spread, Gradient dynamical systems; Stiefel manifold, Joint PCA-MCA, Joint PSA-MSA, Oja's rule",

author = "Hasan, {Mohammed A.}",

year = "2009",

doi = "10.1109/ISCAS.2009.5118350",

language = "English (US)",

isbn = "9781424438280",

series = "Proceedings - IEEE International Symposium on Circuits and Systems",

pages = "2665--2668",

booktitle = "2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009",

note = "2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009 ; Conference date: 24-05-2009 Through 27-05-2009",

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T1 - Computing extreme subspaces using Mirsky theorem

AU - Hasan, Mohammed A.

PY - 2009

Y1 - 2009

N2 - Extreme eigenpairs computation is of considerable interest in signal processing and estimation. Thus problem of simultaneous computation of the smallest and largest eigenvalues and the corresponding eigenvectors of a symmetric matrix is considered. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Dynamical systems that converge to extreme eigenvectors are derived from necessary optimality conditions which are given in terms of a gradient of certain cost functions over a Stiefel manifold. Numerical examples are given to examine the convergence.

AB - Extreme eigenpairs computation is of considerable interest in signal processing and estimation. Thus problem of simultaneous computation of the smallest and largest eigenvalues and the corresponding eigenvectors of a symmetric matrix is considered. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Dynamical systems that converge to extreme eigenvectors are derived from necessary optimality conditions which are given in terms of a gradient of certain cost functions over a Stiefel manifold. Numerical examples are given to examine the convergence.

KW - Eigenvalue spread

KW - Gradient dynamical systems; Stiefel manifold

KW - Joint PCA-MCA

KW - Joint PSA-MSA

KW - Oja's rule

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UR - http://www.scopus.com/inward/citedby.url?scp=70350153889&partnerID=8YFLogxK

U2 - 10.1109/ISCAS.2009.5118350

DO - 10.1109/ISCAS.2009.5118350

M3 - Conference contribution

AN - SCOPUS:70350153889

SN - 9781424438280

T3 - Proceedings - IEEE International Symposium on Circuits and Systems

SP - 2665

EP - 2668

BT - 2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009

T2 - 2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009

Y2 - 24 May 2009 through 27 May 2009

ER -

Computing extreme subspaces using Mirsky theorem

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