On the Stability of Gauss-Jordan Elimination with Pivoting 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. CACM January, 1975 Peters, G. Wilkinson, J. H. Gauss-Jordan algorithm, Gaussian elimination, back-substitution, backward error analysis, bounds for error in solution, bound for residual 5.11 5.14 CA750104 JB January 12, 1978 10:44 AM 2807 5 2807 2807 5 2807 2807 5 2807