Error Analysis of Gaussian Elimination Method for Solving System of Linear Algebraic Equations
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 A)z = 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1971
- Accession Number
- AD0739891
Entities
People
- Nai-kuan Tsao
Organizations
- Air Force Research Laboratory