Minor and major subspace computation of large matrices

Mohammed A Hasan, Ali A. Hasan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Large matrices arise in many formulations in signal processing and control. In this paper, a Rayleigh quotient iteration (RQI) method for locating the minimum eigenpair for symmetric positive definite matrix pencil has been developed. This method has a cubic convergence rate and does not require computation of matrix inversion. The core procedure is based on a modified Rayleigh quotient iteration (MRQI) which uses a line search (exact or approximate) to determine a vector of steepest descent. As a special case, the proposed algorithm is customized to solve high resolution temporal and spatial frequency tracking problems. 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.

Original languageEnglish (US)
Pages (from-to)IV/536-IV/539
JournalProceedings - IEEE International Symposium on Circuits and Systems
Volume4
DOIs
StatePublished - Jan 1 2002

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