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Using Hybrid CPU-GPU Platforms to Accelerate the Computation of the Matrix Sign Function

Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Orti, Alfredo Remon
Fakultat fur Mathematik, Chemnitz University of Technology, D-09107 Chemnitz, Germany
Euro-Par 2009, Parallel Processing Workshops, Lecture Notes in Computer Science, 2010, Volume 6043/2010, 132-139

@conference{benner2010using,

   title={Using Hybrid CPU-GPU Platforms to Accelerate the Computation of the Matrix Sign Function},

   author={Benner, P. and Ezzatti, P. and Quintana-Ort{‘i}, E. and Rem{‘o}n, A.},

   booktitle={Euro-Par 2009–Parallel Processing Workshops},

   pages={132–139},

   year={2010},

   organization={Springer}

}

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We investigate the numerical computation of the matrix sign function of large-scale dense matrices. This is a common task in various application areas. The main computational work in Newton’s iteration for the matrix sign function consits of matrix inversion. Therefore, we investigate the performance of two approaches for matrix inversion based on Gaussian (LU factorization) and Gauss-Jordan eliminations. The target architecture is a current general-purpose multi-core processor connected to a graphics processor. Parallelism is extracted in both processors by linking sequential versions of the codes with multi-threaded implementations of BLAS. Our results on a system with two Intel QuadCore processors and an nvidia Tesla C1060 illustrate the performance and scalability attained by the codes on this system.
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