Accession Number : ADA313644

Title :   Low Rank Determination Using Least Squares.

Descriptive Note : Final rept. Jun-Aug 95,

Corporate Author : NAVAL AIR WARFARE CENTER AIRCRAFT DIV PATUXENT RIVER MD

Personal Author(s) : Turner, Peter R.

PDF Url : ADA313644

Report Date : 05 AUG 1995

Pagination or Media Count : 20

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.

Descriptors :   *MATRICES(MATHEMATICS), *LEAST SQUARES METHOD, ALGORITHMS, ACCURACY, MATHEMATICAL PROGRAMMING, APPROXIMATION(MATHEMATICS), ERROR ANALYSIS, PERTURBATIONS, FAULT TOLERANCE, FLOATING POINT OPERATION, ORTHOGONALITY, NORMAL DISTRIBUTION.

Subject Categories : Numerical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE