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Hierarchical Approach for Deriving a Reproducible LU factorization on GPUs

Abstract

We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we provide Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via inexpensive iterative refinement. Following a bottom-up approach, we finally construct a reproducible implementation of the LU factorization for GPUs, which can easily accommodate partial pivoting for stability and be eventually integrated into a (blocked) high performance and stable algorithm for the LU factorization.
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Dates and versions

hal-01382645 , version 1 (17-10-2016)

Identifiers

  • HAL Id : hal-01382645 , version 1

Cite

Roman S Iakymchuk, Stef S Graillat, David Defour, Enrique S Quintana-Ortí. Hierarchical Approach for Deriving a Reproducible LU factorization on GPUs. The Numerical Reproducibility at Exascale (NRE16) workshop held as part of the Supercomputing Conference (SC16), Nov 2016, Salt Lake City, UT, United States. ⟨hal-01382645⟩
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