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Parallel Communication-Avoiding Algorithm for Triangular Matrix Inversion on Homogeneous and Heterogeneous Platforms

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Abstract

We address in this paper the parallelization of a recursive algorithm for large scale triangular matrix inversion based on the ‘Divide and Conquer’ (D&C) paradigm. A set of different versions of an original sequential algorithm are first presented. A theoretical performance study permits to establish an accurate comparison between the designed algorithms. Afterwards, we develop in the second part of the paper, an optimal parallel avoiding-communication algorithm for a given number of available homogeneous and heterogeneous processors. To reach this target, we use a so called ‘non equitable and incomplete’ version of the D&C paradigm consisting in recursively decomposing the original problem into two sub-problems of non equal sizes, then decomposing only one sub-problem in the same previous manner. The theoretical study is validated by a series of experiments achieved on three target platforms, namely an 8-core shared memory machine, a distributed memory cluster and a heterogeneous CPU-GPU cluster. The obtained results permit to illustrate the interest of the contribution.

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Acknowledgments

We address our deep thanks to Dr. N. Jaïdane for his invaluable help and an anonymous referee for his judicious comments and suggestions

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Authors and Affiliations

  1. Faculty of Sciences of Tunis, University of Tunis El Manar, Manar II, 2092 , Tunis, Tunisia

    Ryma Mahfoudhi & Zaher Mahjoub

  2. Higher School of Sciences and Techniques of Tunis, 1008 , Montfleury, Tunis, Tunisia

    Wahid Nasri

Authors
  1. Ryma Mahfoudhi
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  2. Zaher Mahjoub
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  3. Wahid Nasri
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Corresponding author

Correspondence to Ryma Mahfoudhi.

Additional information

This paper is based on two previous communications published in RenPar’20/SympA’14/CFSE 8, Saint-Malo, France, 2011 and CANA, Wroklaw, Poland, 2012 [28, 29].

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Mahfoudhi, R., Mahjoub, Z. & Nasri, W. Parallel Communication-Avoiding Algorithm for Triangular Matrix Inversion on Homogeneous and Heterogeneous Platforms. Int J Parallel Prog 43, 631–655 (2015). https://doi.org/10.1007/s10766-014-0310-0

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