Numerische Mathematik

, Volume 16, Issue 4, pp 360–361 | Cite as

Monitoring the numerical stability of Gaussian elimination

  • P. A. Businger


Complete pivoting is known to be numerically preferable to partial pivoting for solving systems of linear algebraic equations by Gaussian elimination. However, partial pivoting requires less computational work. Hence we should like to use partial pivoting provided we can easily recognize numerical difficulties. We propose an effective and inexpensive test for this purpose.


Mathematical Method Algebraic Equation Numerical Stability Linear Algebraic Equation Gaussian Elimination 
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  1. 1.
    Forsythe, G. E., Moler, C. B.: Computer solution of linear algebraic systems. Prentice Hall 1967 Section 21.Google Scholar
  2. 2.
    Kahan, W.: Numerical linear algebra. Canad. Math. Bulletin9, 757–801 (1966). Section 4.Google Scholar
  3. 3.
    Wilkinson, J. H.: Rounding errors in algebraic processes. Prentice Hall 1963 Chapter 3, Section 16.Google Scholar
  4. 4.
    Businger, P. A.: MIDAS—solution of linear algebraic equations. Numerical Mathematics Program Library Project, Bell Telephone Laboratories, Inc., Murray Hill, New Jersey.Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • P. A. Businger
    • 1
  1. 1.Bell Telephone LaboratoriesMurray HillUSA

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