Accession Number : ADA313547

Title :   Gauss Elimination: Workhorse of Linear Algebra.

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 : ADA313547

Report Date : 05 AUG 1995

Pagination or Media Count : 52

Abstract : This report brings together many different aspects of Gauss elimination. The basic Gauss elimination (GE) algorithm is a fundamental tool of linear algebra computation for solving systems, computing determinants and determining the rank of matrix. All of these are discussed in varying contexts. These include different arithmetic or algebraic setting such as integer arithmetic or polynomial rings as well as conventional real (floating-point) arithmetic. These have effects on both accuracy and complexity analyses of the algorithm. These, too, are covered here. The impact of modern parallel computer architecture on GE is also included. Finally, GE is considered within the context of 'noisy' matrices. The effect of the noise in matrix entries on the effective rank of the matrix is the central aspect considered here.

Descriptors :   *MATRICES(MATHEMATICS), *INTEGER PROGRAMMING, *FLOATING POINT OPERATION, ALGORITHMS, LINEAR SYSTEMS, COMPUTATIONS, LINEAR PROGRAMMING, ACCURACY, PARALLEL PROCESSING, APPROXIMATION(MATHEMATICS), ERROR ANALYSIS, POLYNOMIALS, LEAST SQUARES METHOD, VECTOR ANALYSIS, SYSTEMS ANALYSIS, NUMERICAL METHODS AND PROCEDURES, ARITHMETIC, FAULT TOLERANCE, DETERMINANTS(MATHEMATICS), SYMBOLIC PROGRAMMING, RINGS(MATHEMATICS).

Subject Categories : Numerical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE