Simple, Effective Computation of Principal Eigen-Vectors and Their Eigenvalues and Application to High-Resolution Estimation of Frequencies

Abstract

We present the results of an investigation of the Prony-Lanczos method and the power method for simple computation of approximations to a few eigenvectors and eigenvalues of a Hermitian matrix. We are motivated by realization of high resolution signal processing in an integrated circuit. The computational speeds of the above methods are analyzed. They are completely dependent on the speed of a matrix vector product operation. If only a few eigenvalues or eigenvectors are needed, the suggested methods can substitute for the slower methods of the LINPACK or EISPACK subroutine libraries. The accuracies of the suggested methods are evaluated using matrices formed from simulated data consisting of two sinusoids plus gaussian noise. Comparisons are made with the corresponding eigenvalues and eigenvectors obtained using LINPACK. Also the accuracies of frequency estimates obtained from the eigenvectors are compared.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA242810

Entities

People

  • Costas D. Melissinos
  • Donald W. Tufts

Organizations

  • University of Rhode Island

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computations
  • Covariance
  • Data Science
  • Eigenvalues
  • Eigenvectors
  • Electrical Engineering
  • Engineering
  • Equations
  • Factor Analysis
  • High Resolution
  • Military Research
  • Rhode Island
  • Signal Processing
  • Statistics
  • Universities

Fields of Study

  • Engineering
  • Physics

Readers

  • Linear Algebra
  • Radar Systems Engineering.