NDLI: Fast algorithm for computing the maximum and minimum eigenpairs of large matrices

Content Provider	IEEE Xplore Digital Library
Author	Hasan, M.A.
Copyright Year	2002
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN, USA (Hasan, M.A.)
Abstract	Computing all the eigenvalues and eigenvectors of a large matrix is a time-consuming operation. There are many applications in signal processing, control, and applied mathematics that require only the minimum and/or maximum eigenpairs. New methods for computing the smallest and largest eigenvalues of a symmetric matrix are developed. These methods are modifications of the Rayleigh quotient iteration aimed at circumventing some drawbacks of that method such as its non or slow convergence. In this approach, the Rayleigh quotient is sequentially minimized over several orthogonal vectors. At each iteration, a vector is formed from a linear combination of the current iteration and an orthogonal vector that is derived from a gradient of a Ritz functional. The proposed methods have global and cubic convergence rate. These methods are also generalized to solve high resolution temporal and spatial frequency tracking problems. The eigenstructure tracking algorithm has update complexity O(n/sup 2/p), where n is the data dimension and p is the dimension of the minor or major subspaces. The performance of these algorithms is tested with several examples. Simulations involving large matrices have shown that the convergence behavior is independent of the size of the matrices.
Sponsorship	IEEE Signal Process. Soc
Starting Page	465
Ending Page	469
File Size	412710
Page Count	5
File Format	PDF
ISBN	0780375513
DOI	10.1109/SAM.2002.1191083
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-08-06
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Signal processing algorithms Symmetric matrices Convergence Vectors Eigenvalues and eigenfunctions Process control Mathematics Spatial resolution Frequency Testing
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in