On the stability of Gauss-Jordan elimination with pivoting

Authors:
G. Peters;J. H. Wilkinson
Affiliations:
Department of Trade and Industry, Teddington, Middlesex, England;Department of Trade and Industry, Teddington, Middlesex, England
Venue:
Communications of the ACM
Year:
1975

Citing 3
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Abstract

The stability of the Gauss-Jordan algorithm with partial pivoting for the solution of general systems of linear equations is commonly regarded as suspect. It is shown that in many respects suspicions are unfounded, and in general the absolute error in the solution is strictly comparable with that corresponding to Gaussian elimination with partial pivoting plus back substitution. However, when A is ill conditioned, the residual corresponding to the Gauss-Jordan solution will often be much greater than that corresponding to the Gaussian elimination solution.