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Dense Linear System: A Parallel Self-verified Solver

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Abstract

This article presents a parallel self-verified solver for dense linear systems of equations. This kind of solver is commonly used in many different kinds of real applications which deal with large matrices. Nevertheless, two key problems appear to limit the use of linear system solvers to a more extensive range of real applications: solution correctness and high computational cost. In order to solve the first one, verified computing would be an interesting choice. An algorithm that uses this concept is able to find a highly accurate and automatically verified result providing more reliability. However, the performance of these algorithms quickly becomes a drawback. Aiming at a better performance, parallel computing techniques were employed. Two main parts of this method were parallelized: the computation of the approximate inverse of matrix A and the preconditioning step. The results obtained show that these optimizations increase significantly the overall performance.

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Authors and Affiliations

  1. Faculdade de Informática, PUCRS, Avenida Ipiranga, 6681 Prédio 32 sala 507, Porto Alegre, Brazil

    Mariana Luderitz Kolberg, Luiz Gustavo Fernandes & Dalcidio Moraes Claudio

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  1. Mariana Luderitz Kolberg
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  2. Luiz Gustavo Fernandes
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  3. Dalcidio Moraes Claudio
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Correspondence to Mariana Luderitz Kolberg.

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Kolberg, M.L., Fernandes, L.G. & Claudio, D.M. Dense Linear System: A Parallel Self-verified Solver. Int J Parallel Prog 36, 412–425 (2008). https://doi.org/10.1007/s10766-007-0058-x

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  • DOI: https://doi.org/10.1007/s10766-007-0058-x

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