@**inproceedings**{RISC2391,author = {C. Limongelli and R. Pirastu},

title = {{Exact Solution of Linear Equation Systems over Rational Numbers by Parallel p-Adic Arithmetic}},

booktitle = {{Procs. CONPAR94-VAPP VI Linz}},

language = {english},

abstract = {We describe a parallel implementation of an algorithm for solving
systems of linear equations over the field of rational numbers based
on Gaussian elimination. The rationals are represented by truncated
$p$-adic expansion. This approach permits us to do error free
computations directly over the rationals without converting the system
to an equivalent one over the integers.
The parallelization is based on a multiple homomorphic image technique
and the result is recovered by a parallel version of the Chinese
remainder algorithm. Using a MIMD machine, we compare the proposed
implementation with the classical modular arithmetic, showing that
truncated $p$-adic arithmetic is a feasible tool for solving systems
of linear equations. The proposed implementation leads to a speedup
up to seven by ten processors with respect to the sequential
implementation.},

series = {Lecture Notes in Comput. Sci.},

volume = {854},

pages = {313--323},

isbn_issn = {ISBN: 3-540-58430-7},

year = {1994},

editor = {B. Buchberger and J. Volkert},

refereed = {yes},

length = {11}

}