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An Analysis of Reordering Algorithms to Reduce the Computational Cost of the Jacobi-Preconditioned CG Solver Using High-Precision Arithmetic

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Computational Science and Its Applications – ICCSA 2017 (ICCSA 2017)

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Abstract

Several heuristics for bandwidth and profile reductions have been proposed since the 1960s. In systematic reviews, 133 heuristics applied to these problems have been found. The results of these heuristics have been analyzed so that, among them, 13 were selected in a manner that no simulation or comparison showed that these algorithms could be outperformed by any other algorithm in the publications analyzed, in terms of bandwidth or profile reductions and also considering the computational costs of the heuristics. Therefore, these 13 heuristics were selected as the most promising low-cost methods to solve these problems. Based on this experience, this article reports that in certain cases no heuristic for bandwidth or profile reduction can reduce the computational cost of the Jacobi-preconditioned Conjugate Gradient Method when using high-precision numerical computations.

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Acknowledgments

This work was undertaken with the support of the Fapemig - Fundação de Amparo à Pesquisa do Estado de Minas Gerais. The authors would like to thank respectively Prof. Dr. Dragan Urosevic, from the Mathematical Institute SANU, and Prof. Dr. Fei Xiao, from Beepi, for sending us the VNS-band executable programs, and the source code of the FNCHC heuristic. In addition, we would like to thank the reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Universidade Federal de Lavras, Lavras, Minas Gerais, Brazil

    Sanderson L. Gonzaga de Oliveira & Júnior Assis Barreto Bernardes

  2. Instituto Nacional de Pesquisas Espaciais, São José dos Campos, São Paulo, Brazil

    Guilherme Oliveira Chagas

Authors
  1. Sanderson L. Gonzaga de Oliveira
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  2. Guilherme Oliveira Chagas
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  3. Júnior Assis Barreto Bernardes
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Correspondence to Sanderson L. Gonzaga de Oliveira .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Gonzaga de Oliveira, S.L., Chagas, G.O., Bernardes, J.A.B. (2017). An Analysis of Reordering Algorithms to Reduce the Computational Cost of the Jacobi-Preconditioned CG Solver Using High-Precision Arithmetic. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10404. Springer, Cham. https://doi.org/10.1007/978-3-319-62392-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-62392-4_1

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