You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination
Erwin H. Bareiss
Mathematics of Computation
Vol. 22, No. 103 (Jul., 1968), pp. 565-578
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2004533
Page Count: 14
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
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.
Mathematics of Computation © 1968 American Mathematical Society