A hybrid Hermitian general eigenvalue solver

Raffaele Solca, Thomas C. Schulthess, Azzam Haidar, Stanimire Tomov, Ichitaro Yamazaki, Jack Dongarra
Institute for Theoretical Physics ETHZ, Swiss National Supercomputing Centre (ETHZ/CSCS)
arXiv:1207.1773v1 [cs.NA] (7 Jul 2012)


   author={Solc{‘a}}, R. and {Schulthess}, T.~C. and {Haidar}, A. and {Tomov}, S. and {Yamazaki}, I. and {Dongarra}, J.},

   title={"{A hybrid Hermitian general eigenvalue solver}"},

   journal={ArXiv e-prints},




   keywords={Computer Science – Numerical Analysis},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized eigenvalue problems must be solved many times. The small size of the problems limits the scalability on a distributed memory system, hence they can benefit from the massive computational performance concentrated on a single node, hybrid GPU-CPU system. However, new algorithms that efficiently exploit heterogeneity and massive parallelism of not just GPUs, but of multi/many-core CPUs as well are required. Addressing these demands, we implemented a novel Hermitian general eigensolver algorithm. This algorithm is based on a standard eigenvalue solver, and existing algorithms can be used. The resulting eigensolvers are state-of-the-art in HPC, significantly outperforming existing libraries. We analyze their performance impact on applications of interest, when different fractions of eigenvectors are needed by the host electronic structure code.
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