Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem

Mark Gates; Azzam Haidar; Jack Dongarra

doi:10.1007/978-3-319-17353-5_16

Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem

Mark Gates, Azzam Haidar, Jack Dongarra

Computer Science and Mathematics Div

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

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.

Original language	English
Title of host publication	High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers
Editors	Osni Marques, Michel Dayde, Kengo Nakajima
Publisher	Springer Verlag
Pages	182-191
Number of pages	10
ISBN (Print)	9783319173528
DOIs	https://doi.org/10.1007/978-3-319-17353-5_16
State	Published - 2015
Event	11th International Conference on High Performance Computing for Computational Science, VECPAR 2014 - Eugene, United States Duration: Jun 30 2014 → Jul 3 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8969
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Conference on High Performance Computing for Computational Science, VECPAR 2014
Country/Territory	United States
City	Eugene
Period	06/30/14 → 07/3/14

Funding

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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10.1007/978-3-319-17353-5_16

Cite this

Gates, M., Haidar, A., & Dongarra, J. (2015). Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem. In O. Marques, M. Dayde, & K. Nakajima (Eds.), High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers (pp. 182-191). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8969). Springer Verlag. https://doi.org/10.1007/978-3-319-17353-5_16

Gates, Mark ; Haidar, Azzam ; Dongarra, Jack. / Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem. High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers. editor / Osni Marques ; Michel Dayde ; Kengo Nakajima. Springer Verlag, 2015. pp. 182-191 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Gates, M, Haidar, A & Dongarra, J 2015, Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem. in O Marques, M Dayde & K Nakajima (eds), High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8969, Springer Verlag, pp. 182-191, 11th International Conference on High Performance Computing for Computational Science, VECPAR 2014, Eugene, United States, 06/30/14. https://doi.org/10.1007/978-3-319-17353-5_16

Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem. / Gates, Mark; Haidar, Azzam; Dongarra, Jack.
High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers. ed. / Osni Marques; Michel Dayde; Kengo Nakajima. Springer Verlag, 2015. p. 182-191 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8969).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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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Gates M, Haidar A, Dongarra J. Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem. In Marques O, Dayde M, Nakajima K, editors, High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers. Springer Verlag. 2015. p. 182-191. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-17353-5_16

Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem

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