An algorithm for computing the pisarenko vector

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

Abstract

The problem of computing the minimum eigenvector (the Pisarenko vector) of a covariance matrix is of considerable interest in signal processing and computational linear algebra. In this paper, a unified algorithm for computing both the minimum and maximum eigenpairs by simply choosing the proper initial condition is proposed. In particular, the extremum eigenpairs are computed using higher order convergent methods which include the Newton method, the Halley and root iterations. The advantage of these methods is that one can control where the methods converge by choosing a proper initial condition. Some of the methods are implemented using the QR factorization to avoid matrix inversion. By appropriately choosing the initial condition, this approach can also be used to compute the largest eigenpair and thus can be applied for computing the minor and major subspaces of symmetric or hermitian matrices. Procedures such as the double step Newton method for accelerating the developed methods are considered. Several randomly generated test problems are used to evaluate the performance of the methods.

Original languageEnglish (US)
Title of host publication2002 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAME 2002
PublisherIEEE Computer Society
Pages23-27
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

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