Abstract
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.
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References
Forsythe, G. E., Moler, C. B.: Computer solution of linear algebraic systems. Prentice Hall 1967 Section 21.
Kahan, W.: Numerical linear algebra. Canad. Math. Bulletin9, 757–801 (1966). Section 4.
Wilkinson, J. H.: Rounding errors in algebraic processes. Prentice Hall 1963 Chapter 3, Section 16.
Businger, P. A.: MIDAS—solution of linear algebraic equations. Numerical Mathematics Program Library Project, Bell Telephone Laboratories, Inc., Murray Hill, New Jersey.
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Businger, P.A. Monitoring the numerical stability of Gaussian elimination. Numer. Math. 16, 360–361 (1971). https://doi.org/10.1007/BF02165006
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DOI: https://doi.org/10.1007/BF02165006