Abstract
We present a multi-threaded solver for symmetric positive definite linear systems where the coefficient matrix of the problem features a bordered-band non-zero pattern. The algorithms that implement this approach heavily rely on a compact storage format, tailored for this type of matrices, that reduces the memory requirements, produces a regular data access pattern, and allows to cast the bulk of the computations in terms of efficient kernels from the Level-3 and Level-2 BLAS. The efficiency of our approach is illustrated by numerical experiments.
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Acknowledgments
The researcher from Universidad Jaime I was supported by the CICYT project TIN2011-23283 of the Ministerio de Economía y Competitividad and FEDER. We would like to thank Matthias Bollhöfer, from TU Braunschweig, for his help during the evaluation of these codes.
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Benner, P., Ezzatti, P., Quintana-Ortí, E.S., Remón, A. (2016). A Parallel Multi-threaded Solver for Symmetric Positive Definite Bordered-Band Linear Systems. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2015. Lecture Notes in Computer Science(), vol 9573. Springer, Cham. https://doi.org/10.1007/978-3-319-32149-3_10
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DOI: https://doi.org/10.1007/978-3-319-32149-3_10
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