Fast algorithm for computating the maximum and minimum Eigenpairs of large matrices

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Computing all the eigenvalues and eigenvectors of a large matrix is a time-consuming operation. There are many applications in signal pmssing, control. and applied mathematics that require only the minimum and/or maximum eigenpairs. In this paper, new methods for computing the smallest and largest eigenvalues of symmetric matrix are developed. These methods are modifications of the Rayleigh quotient iteration aimed at citrumventing some drawbacks of that method such as its non or slow convergence. In this approach, the Rayleigh quotient is squentially minimized over several orthogonal vectors. At each iterate, a vector is formed fmm a linear combination of the current iterate and an orthogonal vector that is derived fmm a gradient of a Ritz functional. The pmpsed methods have global and cubic convergence rate. These methods are also generalized to solve high resolution temporal and spatial frequency tracking pmblems. The eigenstructure tracking algorithm has update complexity O(n2p). 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.

Original languageEnglish (US)
Title of host publication2002 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAME 2002
PublisherIEEE Computer Society
Pages465-469
Number of pages5
ISBN (Electronic)0780375513
DOIs
StatePublished - Jan 1 2002
EventIEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2002 - Rosslyn, United States
Duration: Aug 4 2002Aug 6 2002

Publication series

NameProceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
Volume2002-January
ISSN (Electronic)2151-870X

Other

OtherIEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2002
CountryUnited States
CityRosslyn
Period8/4/028/6/02

Fingerprint Dive into the research topics of 'Fast algorithm for computating the maximum and minimum Eigenpairs of large matrices'. Together they form a unique fingerprint.

  • Cite this

    Hasan, M. A. (2002). Fast algorithm for computating the maximum and minimum Eigenpairs of large matrices. In 2002 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAME 2002 (pp. 465-469). [1191083] (Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop; Vol. 2002-January). IEEE Computer Society. https://doi.org/10.1109/SAM.2002.1191083