GPU-accelerated asynchronous error correction for mixed precision iterative refinement

Authors:
Hartwig Anzt;Piotr Luszczek;Jack Dongarra;Vincent Heuveline
Affiliations:
Karlsruhe Institute of Technology, Karlsruhe, Germany;University of Tennessee, Knoxville;University of Tennessee, Knoxville, USA,Oak Ridge National Laboratory, Oak Ridge, USA, University of Manchester, Manchester, UK;Karlsruhe Institute of Technology, Karlsruhe, Germany
Venue:
Euro-Par'12 Proceedings of the 18th international conference on Parallel Processing
Year:
2012

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Abstract

In hardware-aware high performance computing, block- asynchronous iteration and mixed precision iterative refinement are two techniques that may be used to leverage the computing power of SIMD accelerators like GPUs in the iterative solution of linear equation systems. Although they use a very different approach for this purpose, they share the basic idea of compensating the convergence properties of an inferior numerical algorithm by a more efficient usage of the provided computing power. In this paper, we analyze the potential of combining both techniques. Therefore, we derive a mixed precision iterative refinement algorithm using a block-asynchronous iteration as an error correction solver, and compare its performance with a pure implementation of a block-asynchronous iteration and an iterative refinement method using double precision for the error correction solver. For matrices from the University of Florida Matrix collection, we report the convergence behaviour and provide the total solver runtime using different GPU architectures.