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.

Access to Document

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)).

@inproceedings{b27578f34e054a4c96b4bbdf9c73b906,

title = "Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem",

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.",

author = "Mark Gates and Azzam Haidar and Jack Dongarra",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 11th International Conference on High Performance Computing for Computational Science, VECPAR 2014 ; Conference date: 30-06-2014 Through 03-07-2014",

year = "2015",

doi = "10.1007/978-3-319-17353-5\_16",

language = "English",

isbn = "9783319173528",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "182--191",

editor = "Osni Marques and Michel Dayde and Kengo Nakajima",

booktitle = "High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers",

}

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

TY - GEN

T1 - Accelerating computation of eigenvectors in the dense nonsymmetric eigenvalue problem

AU - Gates, Mark

AU - Haidar, Azzam

AU - Dongarra, Jack

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84942582704

U2 - 10.1007/978-3-319-17353-5_16

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

M3 - Conference contribution

AN - SCOPUS:84942582704

SN - 9783319173528

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 182

EP - 191

BT - High Performance Computing for Computational Science - VECPAR 2014 - 11th International Conference, Revised Selected Papers

A2 - Marques, Osni

A2 - Dayde, Michel

A2 - Nakajima, Kengo

PB - Springer Verlag

T2 - 11th International Conference on High Performance Computing for Computational Science, VECPAR 2014

Y2 - 30 June 2014 through 3 July 2014

ER -

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

Abstract

Publication series

Conference

Funding

Access to Document

Other files and links

Fingerprint

Cite this