A parallel tiled solver for dense symmetric indefinite systems on multicore architectures

Marc Baboulin; Dulceneia Becker; Jack Dongarra

doi:10.1109/IPDPS.2012.12

A parallel tiled solver for dense symmetric indefinite systems on multicore architectures

Marc Baboulin, Dulceneia Becker, Jack Dongarra

Computer Science and Mathematics Div

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

13 Scopus citations

Abstract

We describe an efficient and innovative parallel tiled algorithm for solving symmetric indefinite systems on multicore architectures. This solver avoids pivoting by using a multiplicative preconditioning based on symmetric randomization. This randomization prevents the communication overhead due to pivoting, is computationally inexpensive and requires very little storage. Following randomization, a tiled factorization is used that reduces synchronization by using static or dynamic scheduling. We compare Gflop/s performance of our solver with other types of factorizations on a current multicore machine and we provide tests on accuracy using LAPACK test cases.

Original language	English
Title of host publication	Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012
Pages	14-24
Number of pages	11
DOIs	https://doi.org/10.1109/IPDPS.2012.12
State	Published - 2012
Event	2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012 - Shanghai, China Duration: May 21 2012 → May 25 2012

Publication series

Name	Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012

Conference

Conference	2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012
Country/Territory	China
City	Shanghai
Period	05/21/12 → 05/25/12

Keywords

dense linear algebra
randomized algorithms
symmetric indefinite systems
tiled factorization

Access to Document

10.1109/IPDPS.2012.12

Cite this

Baboulin, M., Becker, D., & Dongarra, J. (2012). A parallel tiled solver for dense symmetric indefinite systems on multicore architectures. In Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012 (pp. 14-24). Article 6267820 (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012). https://doi.org/10.1109/IPDPS.2012.12

Baboulin, Marc ; Becker, Dulceneia ; Dongarra, Jack. / A parallel tiled solver for dense symmetric indefinite systems on multicore architectures. Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012. 2012. pp. 14-24 (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012).

@inproceedings{6b4e519584ec4a20a020ab0d8c86a896,

title = "A parallel tiled solver for dense symmetric indefinite systems on multicore architectures",

abstract = "We describe an efficient and innovative parallel tiled algorithm for solving symmetric indefinite systems on multicore architectures. This solver avoids pivoting by using a multiplicative preconditioning based on symmetric randomization. This randomization prevents the communication overhead due to pivoting, is computationally inexpensive and requires very little storage. Following randomization, a tiled factorization is used that reduces synchronization by using static or dynamic scheduling. We compare Gflop/s performance of our solver with other types of factorizations on a current multicore machine and we provide tests on accuracy using LAPACK test cases.",

keywords = "dense linear algebra, randomized algorithms, symmetric indefinite systems, tiled factorization",

author = "Marc Baboulin and Dulceneia Becker and Jack Dongarra",

year = "2012",

doi = "10.1109/IPDPS.2012.12",

language = "English",

isbn = "9780769546759",

series = "Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012",

pages = "14--24",

booktitle = "Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012",

note = "2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012 ; Conference date: 21-05-2012 Through 25-05-2012",

}

Baboulin, M, Becker, D & Dongarra, J 2012, A parallel tiled solver for dense symmetric indefinite systems on multicore architectures. in Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012., 6267820, Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012, pp. 14-24, 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012, Shanghai, China, 05/21/12. https://doi.org/10.1109/IPDPS.2012.12

A parallel tiled solver for dense symmetric indefinite systems on multicore architectures. / Baboulin, Marc; Becker, Dulceneia; Dongarra, Jack.
Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012. 2012. p. 14-24 6267820 (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012).

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

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AB - We describe an efficient and innovative parallel tiled algorithm for solving symmetric indefinite systems on multicore architectures. This solver avoids pivoting by using a multiplicative preconditioning based on symmetric randomization. This randomization prevents the communication overhead due to pivoting, is computationally inexpensive and requires very little storage. Following randomization, a tiled factorization is used that reduces synchronization by using static or dynamic scheduling. We compare Gflop/s performance of our solver with other types of factorizations on a current multicore machine and we provide tests on accuracy using LAPACK test cases.

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Baboulin M, Becker D, Dongarra J. A parallel tiled solver for dense symmetric indefinite systems on multicore architectures. In Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012. 2012. p. 14-24. 6267820. (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012). doi: 10.1109/IPDPS.2012.12

A parallel tiled solver for dense symmetric indefinite systems on multicore architectures

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