Exact solution of linear equations usingP-adic expansions |
| |
Authors: | John D Dixon |
| |
Institution: | (1) Department of Mathematics and Statistics, Carleton University, K1S 5B6 Ottawa, Canada |
| |
Abstract: | Summary A method is described for computing the exact rational solution to a regular systemAx=b of linear equations with integer coefficients. The method involves: (i) computing the inverse (modp) ofA for some primep; (ii) using successive refinements to compute an integer vector
such that
(modp
m
) for a suitably large integerm; and (iii) deducing the rational solutionx from thep-adic approximation
. For matricesA andb with entries of bounded size and dimensionsn×n andn×1, this method can be implemented in timeO(n
3(logn)2) which is better than methods previously used.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (Grant No. A 7171) |
| |
Keywords: | (MR 1980) AMS(MOS) 65F05 15A06 10M10 10A30 CR: 5 14 |
本文献已被 SpringerLink 等数据库收录! |