Abstract
The optimization of dense linear algebra operations is a fundamental task in the solution of many scientific computing applications. The Roofline Model is a tool that provides an estimation of the performance that a computational kernel can attain on a hardware platform. Therefore, the RM can be used to investigate whether a computational kernel can be further accelerated. We present an approach, based on the RM, to optimize the algorithmic parameters of dense linear algebra kernels. In particular, we perform a basic analysis to identify the optimal values for the kernel parameters. As a proof-of-concept, we apply this technique to optimize a blocked algorithm for matrix inversion via Gauss-Jordan elimination. In addition, we extend this technique to multi-block computational kernels. An experimental evaluation validates the method and shows its convenience. We remark that the results obtained can be extended to other computational kernels similar to Gauss-Jordan elimination such as, e.g., matrix factorizations and the solution of linear least squares problems.
All researchers acknowledge the support from the EHFARS project funded by the German Ministry of Education and Research BMBF.
E.S. Quintana-Ortí—Supported by the CICYT project TIN2014-53495-R of the Ministerio de Economía y Competitividad and FEDER.
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Benner, P., Ezzatti, P., Quintana-Ortí, E.S., Remón, A., Silva, J.P. (2016). Tuning the Blocksize for Dense Linear Algebra Factorization Routines with the Roofline Model. In: Carretero, J., et al. Algorithms and Architectures for Parallel Processing. ICA3PP 2016. Lecture Notes in Computer Science(), vol 10049. Springer, Cham. https://doi.org/10.1007/978-3-319-49956-7_2
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DOI: https://doi.org/10.1007/978-3-319-49956-7_2
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