Exact solution of linear systems over rational numbers by parallel p-adic arithmetic

  • Carla Limongelli
  • Roberto Pirastu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 854)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Carla Limongelli
    • 1
  • Roberto Pirastu
    • 1
  1. 1.Research Institute for Symbolic Computation RISC-LinzJohannes Kepler UniversityLinzAustria

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