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

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