RISC RISC Research Institute for Symbolic Computation  
  • @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}