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Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation

Authors: Mariana Kolberg, Gerd Bohlender, and Dalcidio Claudio

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract

A parallel version of the self-verified method for solving linear systems was presented on PARA and VECPAR conferences in 2006. In this research we propose improvements aiming at a better performance. The idea is to implement an algorithm that uses technologies as MPI communication primitives associated to libraries as LAPACK, BLAS and C-XSC, aiming to provide both self-verification and speed-up at the same time. The algorithms should find an enclosure even for very ill-conditioned problems. In this scenario, a parallel version of a self-verified solver for dense linear systems appears to be essential in order to solve bigger problems. Moreover, the major goal of this research is to provide a free, fast, reliable and accurate solver for dense linear systems.

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Mariana Kolberg, Gerd Bohlender, and Dalcidio Claudio. Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kolberg_et_al:DagSemProc.08021.13,
  author =	{Kolberg, Mariana and Bohlender, Gerd and Claudio, Dalcidio},
  title =	{{Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.13},
  URN =		{urn:nbn:de:0030-drops-14386},
  doi =		{10.4230/DagSemProc.08021.13},
  annote =	{Keywords: Linear systems, result verification, parallel computing}
}

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Improving the Performance of a Verified Linear System Solver Using Optimized Libraries and Parallel Computation

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