2807	 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. Gauss-Jordan algorithm Gaussian elimination back-substitution backward error analysis bounds for error in solution bound for residual
