A Parallel Adaptive Gauss-Jordan Algorithm

  • Authors:
  • N. Melab;E.-G. Talbi;S. Petiton

  • Affiliations:
  • Laboratoire d'Informatique du Littoral, Université du Littoral, BP 719, 3, rue Louis David, 62228, Calais Cedex, France melab@lil.univ-littoral.fr;Laboratoire d'Informatique Fondamentale de Lille (LIFL-CNRS URA 369), Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq cedex, France talbi@lifl.fr;Laboratoire d'Informatique Fondamentale de Lille (LIFL-CNRS URA 369), Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq cedex, France petiton@lifl.fr

  • Venue:
  • The Journal of Supercomputing
  • Year:
  • 2000

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Abstract

This paper presents a parallel adaptive version of the block-based Gauss-Jordan algorithm, utilized to invert large matrices. This version includes a characterization of the workload and a mechanism of its folding/unfolding. Furthermore, this paper proposes a work scheduling strategy and an application-oriented solution for the fault tolerance problem. The application is implemented and experimented with MARS1 in dedicated and non-dedicated environments. The results show that an absolute efficiency of 92% is possible on a cluster of DEC/ALPHA processors interconnected by a Gigaswitch network and an absolute efficiency of 67% can be obtained on an Ethernet network of SUN-Sparc 4 workstations. Moreover, the algorithm is tested on a meta-system including both the two parks of machines. Finally, an out-of-core solution for the algorithm is proposed. This solution allows a gain of 66% of data input operations and reduces the central memory space required for storing the data space of the algorithm by a factor q, where q is the dimension of the matrix to be inverted in terms of data blocks.