Sylvester’s identity and multistep integer-preserving Gaussian elimination
Author:
Abstract
A method is developed which permits integer-preserving elimination in systems of linear equations, A X = B AX = B , such that ( a ) (a) the magnitudes of the coefficients in the transformed matrices are minimized, and ( b ) (b) the computational efficiency is considerably increased in comparison with the corresponding ordinary (single-step) 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 two-step method. The method should also prove superior to the widely used fraction-producing Gaussian elimination when A A is nearly singular.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,Computational Mathematics,Algebra and Number Theory
Link
http://www.ams.org/mcom/1968-22-103/S0025-5718-1968-0226829-0/S0025-5718-1968-0226829-0.pdf
Reference12 articles.
1. E. H. Bareiss, Multistep Integer-Preserving Gaussian Elimination, Argonne National Laboratory Report ANL-7213, May, 1966.
2. E. H. Bareiss, The Root Cubing and the General Root Powering Methods for Finding the Zero of Polynomials, Argonne National Laboratory Report ANL-7344, 1967.
3. J. Boothroyd, “Algorithm 290, linear equations, exact solutions [𝐹4],” Comm. ACM, v. 9, 1966, pp. 683–684.
4. 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. 150–155.
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