Abstract:A method is developed which permits integer-preserving elimination in systems of linear equations, $AX = B$, such that $(a)$ the magnitudes of the coefficients in the transformed matrices are minimized, and $(b)$ 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 $A$ is nearly singular.
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- © Copyright 1968 American Mathematical Society
- Journal: Math. Comp. 22 (1968), 565-578
- MSC: Primary 65.35
- DOI: https://doi.org/10.1090/S0025-5718-1968-0226829-0
- MathSciNet review: 0226829