APPROXIMATE EIGENSYSTEMS OF LARGE COVARIANCE MATRICES.

Abstract

The paper presents a method for obtaining approximate solutions of the algebraic eigenvalue problem for hermitian matrices with a substantial reduction in computation time. The approach is to apply a standard eigenvalue routine to submatrices of the original matrix and use the results to transform the original matrix into one of much lower dimension having eigenvalues approximately equal to the largest eigenvalues of the original matrix. A method of information compression by intrinsic analysis is described. The eigensystem approximation is applied to the intrinsic analysis computations, and explicit formulas are derived for the additional error introduced by the approximation. Results of two specific applications are given, along with tables of reductions in computation time realized using the approximation. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1968
Accession Number
AD0678172

Entities

People

  • Robert B. Roper

Tags

DTIC Thesaurus Topics

  • Compression
  • Computations
  • Covariance
  • Data Science
  • Eigenvalues
  • Information Science
  • Mathematical Analysis
  • Mathematics
  • Standards

Readers

  • Linear Algebra
  • Systems Analysis and Design