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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Sylvester’s identity and multistep integer-preserving Gaussian elimination
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by Erwin H. Bareiss PDF
Math. Comp. 22 (1968), 565-578 Request permission


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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Additional Information
  • © Copyright 1968 American Mathematical Society
  • Journal: Math. Comp. 22 (1968), 565-578
  • MSC: Primary 65.35
  • DOI:
  • MathSciNet review: 0226829