# Sylvester’s identity and multistep integer-preserving Gaussian elimination

@article{Bareiss1968SylvestersIA, title={Sylvester’s identity and multistep integer-preserving Gaussian elimination}, author={Erwin H. Bareiss}, journal={Mathematics of Computation}, year={1968}, volume={22}, pages={565-578} }

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…

## 360 Citations

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