Abstract
In the dense nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient algorithms and fast, Level 3 BLAS. Comparatively, computation of eigenvectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup on multi-core systems. It has thus become a dominant cost in the solution of the eigenvalue problem. To address this, we present improvements for the eigenvector computation to use Level 3 BLAS and parallelize the triangular solves, achieving good parallel scaling and accelerating the overall eigenvalue problem more than three-fold.
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Acknowledgments
The results were obtained in part with the financial support of the Russian Scientific Fund, Agreement N14-11-00190; the National Science Foundation, U.S. Department of Energy, Intel, NVIDIA, and AMD.
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Gates, M., Haidar, A., Dongarra, J. (2015). Accelerating Computation of Eigenvectors in the Dense Nonsymmetric Eigenvalue Problem. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science -- VECPAR 2014. VECPAR 2014. Lecture Notes in Computer Science(), vol 8969. Springer, Cham. https://doi.org/10.1007/978-3-319-17353-5_16
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DOI: https://doi.org/10.1007/978-3-319-17353-5_16
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