Numerische Mathematik

, Volume 54, Issue 5, pp 591–599 | Cite as

Rehabilitation of the Gauss-Jordan algorithm

  • T. J. Dekker
  • W. Hoffmann


In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.

Subject Classifications

AMS(MOS): 65F05, 65G05, 15A06 CR: G1.3 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • T. J. Dekker
    • 1
  • W. Hoffmann
    • 1
  1. 1.Department of Computer SystemsUniversity of AmsterdamAmsterdamThe Netherlands

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