Sylvester's identity and multistep integerpreserving Gaussian elimination
Author:
Erwin H. Bareiss
Journal:
Math. Comp. 22 (1968), 565578
MSC:
Primary 65.35
MathSciNet review:
0226829
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Abstract: A method is developed which permits integerpreserving elimination in systems of linear equations, , such that the magnitudes of the coefficients in the transformed matrices are minimized, and the computational efficiency is considerably increased in comparison with the corresponding ordinary (singlestep) Gaussian elimination. The algorithms presented can also be used for the efficient evaluation of determinants and their leading minors. Explicit algorithms and flow charts are given for the twostep method. The method should also prove superior to the widely used fractionproducing Gaussian elimination when is nearly singular.
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 E. H. Bareiss, The Root Cubing and the General Root Powering Methods for Finding the Zero of Polynomials, Argonne National Laboratory Report ANL7344, 1967.
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 J. Boothroyd, ``Algorithm 290, linear equations, exact solutions ,'' Comm. ACM, v. 9, 1966, pp. 683684.
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 C. L. Dodgson, ``Condensation of determinants, being a new and brief method for computing their arithmetic values,'' Proc. Roy. Soc. Ser. A, v. 15, 1866, pp. 150155.
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 E. Durand, Solutions Numériques des Équations Algébriques. Vol. II: Systèmes de Plusieurs Équations. Valeurs Propres des Matrices, Masson et Cie, Paris, 1961. MR 24 #B1754. MR 0135709 (24:B1754)
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 L. Fox, An Introduction to Numerical Linear Algebra, Clarendon Press, Oxford, 1964. MR 29 #1733. MR 0164436 (29:1733)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196802268290
PII:
S 00255718(1968)02268290
Article copyright:
© Copyright 1968
American Mathematical Society
