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A Parallel Adaptive Gauss-Jordan Algorithm

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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.

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Authors and Affiliations

  1. Laboratoire d'Informatique du Littoral, Université du Littoral, BP 719, 3, rue Louis David, 62228, Calais Cedex, France

    N. Melab

  2. Laboratoire d'Informatique Fondamentale de Lille (LIFL-CNRS URA 369), Université des Sciences et Technologies de Lille, 59655, Villeneuve d'Ascq cedex, France

    E.-G. Talbi

  3. Laboratoire d'Informatique Fondamentale de Lille (LIFL-CNRS URA 369), Université des Sciences et Technologies de Lille, 59655, Villeneuve d'Ascq cedex, France

    S. Petiton

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  1. N. Melab
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Melab, N., Talbi, EG. & Petiton, S. A Parallel Adaptive Gauss-Jordan Algorithm. The Journal of Supercomputing 17, 167–185 (2000). https://doi.org/10.1023/A:1008182404262

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