Research and Advances

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.

Advertisement

Author Archives

Shape the Future of Computing

ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.

Get Involved