Bareiss, Erwin H. Sylvester’s identity and multistep integer-preserving Gaussian elimination. (English) Zbl 0187.09701 Math. Comput. 22, 565-578 (1968). Author’s summary: “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.” Reviewer: J. T. Day Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 91 Documents MSC: 65-XX Numerical analysis Keywords:numerical analysis × Cite Format Result Cite Review PDF Full Text: DOI Link