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Pivot size in gaussian elimination

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Abstract

LetA = (a ij ) be a real n x n matrix such that |a ij | < 1. It has been conjectured by WILKINSON that if the process of Gaussian elimination with complete pivoting is applied to A then all the pivots are less than or equal to n in absolute value. This conjecture is proved forn=4.

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References

  1. Baumert, L., S. W. Golomb, andM. Hall, Jr.: Discovery of a Hadamard matrix of order 92. Bull. Amer. Math. Soc.68, 237–238 (1962).

    Google Scholar 

  2. Cryer, C. W.: Pivot size in Gaussian elimination with complete pivoting. Tech. Report No. 729, Math. Res. Ctr., U.S. Army, University of Wisconsin, 1967.

  3. Eberlein, P. J.: Some remarks on the Van der Waerden conjecture. Notices Amer. Math. Soc.14, 242 (1967).

    Google Scholar 

  4. Forsythe, G. E., andC. B. Moler: Computer solution of linear algebraic systems. Englewood Cliffs: Prentice-Hall 1967.

    Google Scholar 

  5. Gantmacher, F. R.: The theory of matrices, vol. 1. New York: Chelsea 1959

    Google Scholar 

  6. ——: The theory of matrices, vol. 2. New York: Chelsea 1959

    Google Scholar 

  7. Householder, A. S.: The theory of matrices in numerical analysis. New York: Blaisdell 1964.

    Google Scholar 

  8. Kahan, W.: Numerical linear algebra. Canadian Math. Bull.9, 757–801 (1966).

    Google Scholar 

  9. Ryser, H. J.: Combinatorial mathematics. Mathematical Association of America 1963.

  10. Sharpe, F. R.: The maximum value of a determinant. Bull. Amer. Math. Soc.14, 121–123 (1907).

    Google Scholar 

  11. Tornheim, L.: Maximum third pivot for Gaussian reduction. Tech. Report, Calif. Res. Corp., Richmond, Calif., 1965.

    Google Scholar 

  12. ——: Pivot size in Gauss reduction. Tech. Report, Calif. Res. Corp., Richmond, Calif., February 1964.

    Google Scholar 

  13. Wilkinson, J. H.: Error analysis of direct methods of matrix inversion. J. Assoc. Comp. Mach.8, 281–330 (1961).

    Google Scholar 

  14. ——: The algebraic eigenvalue problem. Oxford: Clarendon Press 1965.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Sciences, University of Wisconsin, 53706, Madison, Wisconsin, USA

    C. W. Cryer

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  1. C. W. Cryer
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Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.

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Cryer, C.W. Pivot size in gaussian elimination. Numer. Math. 12, 335–345 (1968). https://doi.org/10.1007/BF02162514

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  • DOI: https://doi.org/10.1007/BF02162514

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