Low Rank Determination Using Least Squares.

Abstract

In this report we discuss a technique for determining the rank of a matrix of a special type. The matrix is assumed to be composed of a matrix which has very low rank relative to its magnitude and a noise matrix component. The objective is to determine the rank of the 'underlying' matrix. The basic approach explored here is to exploit the observation that the rows of a low rank matrix are linear combinations of a small number of those rows. Therefore if we select 'basis' rows carefully, it should be true that the rows of the noisy matrix can be closely approximated by such linear combinations. The approximation is performed easily in a least squares sense and leads to an algorithm which appears to be quite robust and efficient. Its performance is similar in reliability to the use of SVD-based algorithms but with a cost comparable to Gauss elimination or LU factorization.

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Document Details

Document Type
Technical Report
Publication Date
Aug 05, 1995
Accession Number
ADA313644

Entities

People

  • Peter R. Turner

Organizations

  • Naval Air Warfare Center

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Sensors
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aerial Warfare
  • Aircrafts
  • Algorithms
  • Computational Complexity
  • Computational Science
  • Detection
  • Detectors
  • Elimination
  • Floating Point Operations
  • Fluid Dynamics
  • Mathematics
  • Military Research
  • Normal Distribution
  • Reliability
  • Standards
  • Statistical Analysis
  • United States Naval Academy

Readers

  • Linear Algebra
  • Systems Analysis and Design