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Numerische Mathematik

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

Rehabilitation of the Gauss-Jordan algorithm

  • T. J. Dekker
  • W. Hoffmann
Article

Summary

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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References

  1. 1.
    Businger, P.A.: Monitoring the numerical stability of Gaussian elimination. Numer. Math.16, 360–361 (1971)Google Scholar
  2. 2.
    Dongarra, J.J., Moler, C.F., Bunch, J.R., Stewart, G.W.: LINPACK User's guide. Philadelphia: SIAM 1979Google Scholar
  3. 3.
    Golub, G.H., Van Loan, C.F.: Matrix computations. Oxford: North Oxford Academic 1983Google Scholar
  4. 4.
    Hoffmann, W.: Solving linear systems on a vector computer. J. Comput. Appl. Math.18, 353–367 (1987)Google Scholar
  5. 5.
    Hoffmann, W., Lioen, W.M.: Chapter simultaneous linear equations. Report NM-R8614. In: NUMVEC FORTRAN Library Manual. Amsterdam: Center for Mathematics and Computer Science 1986Google Scholar
  6. 6.
    Peters, G., Wilkinson, J.H.: On the stability of Gauss-Jordan elimination with pivoting. Commun. ACM18, 20–24 (1975)Google Scholar
  7. 7.
    Stewart, G.W.: Introduction to matrix computations. New York London: Academic Press 1973Google Scholar

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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