Accession Number:

AD0739891

Title:

Error Analysis of Gaussian Elimination Method for Solving System of Linear Algebraic Equations

Descriptive Note:

Interim rept.

Corporate Author:

AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OH

Personal Author(s):

Report Date:

1971-12-01

Pagination or Media Count:

30.0

Abstract:

A posteriori forward error analysis is applied to the Gaussian elimination method for solving system of linear algebraic equations of the type Az p. By attributing the generated round-off errors properly to the matrices A and p, it is shown that the computed z satisfies a new perturbed system such that A delta Az p delta p. For large system order n, the upper bounds for delta A and delta p in infinite norm are then shown to be proportional to n squared, instead of n cubed obtained by the usual backward error analysis where round-off errors are attributed totally to the system matrix A. This answers partially some questions raised concerning the discrepancy between the theoretical result and practical observation of the perturbations.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE