research-article

Efficient eigenvalue and singular value computations on shared memory machines

Author:

Bruno LangAuthors Info & Claims

Parallel Computing, Volume 25, Issue 7

Pages 845 - 860

https://doi.org/10.1016/S0167-8191(99)00021-6

Published: 01 July 1999 Publication History

Abstract

We describe two techniques for speeding up eigenvalue and singular value computations on shared memory parallel computers. Depending on the information that is required, different steps in the overall process can be made more efficient. If only the eigenvalues or singular values are sought then the reduction to condensed form may be done in two or more steps to make best use of optimized level-3 BLAS. If eigenvectors and/or singular vectors are required, too, then their accumulation can be speeded up by another blocking technique. The efficiency of the blocked algorithms depends heavily on the values of certain control parameters. We also present a very simple performance model that allows selecting these parameters automatically.

References

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Cited By

Keyes DLtaief HNakatsukasa YSukkari DMohror KArnold DBadia R(2023)High-Performance SVD Partial Spectrum ComputationProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/3581784.3607109(1-12)Online publication date: 12-Nov-2023
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Kabir KHaidar ATomov SDongarra JWatson LWeinbub JSosonkina MThacker W(2015)Performance analysis and design of a hessenberg reduction using stabilized blocked elementary transformations for new architecturesProceedings of the Symposium on High Performance Computing10.5555/2872599.2872616(135-142)Online publication date: 12-Apr-2015
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Efficient eigenvalue and singular value computations on shared memory machines

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Information

Published In

cover image Parallel Computing

Parallel Computing Volume 25, Issue 7

Special issue on parallelization techniques for numerical modelling

July 1999

141 pages

ISSN:0167-8191

Editors:
G. R. Joubert
Technical Univ. of Clausthal, Eindhoven, The Netherlands
,
G. Alefeld,
O. Mahrenholtz,
R. Vollmar

Issue’s Table of Contents

Copyright © Elsevier Science B.V.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 July 1999

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Cited By

Keyes DLtaief HNakatsukasa YSukkari DMohror KArnold DBadia R(2023)High-Performance SVD Partial Spectrum ComputationProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/3581784.3607109(1-12)Online publication date: 12-Nov-2023
https://dl.acm.org/doi/10.1145/3581784.3607109
Sukkari DLtaief HKeyes D(2016)A High Performance QDWH-SVD Solver Using Hardware AcceleratorsACM Transactions on Mathematical Software10.1145/289474743:1(1-25)Online publication date: 13-Aug-2016
https://dl.acm.org/doi/10.1145/2894747
Kabir KHaidar ATomov SDongarra JWatson LWeinbub JSosonkina MThacker W(2015)Performance analysis and design of a hessenberg reduction using stabilized blocked elementary transformations for new architecturesProceedings of the Symposium on High Performance Computing10.5555/2872599.2872616(135-142)Online publication date: 12-Apr-2015
https://dl.acm.org/doi/10.5555/2872599.2872616
Solcà RKozhevnikov AHaidar ATomov SDongarra JSchulthess TKern JVetter J(2015)Efficient implementation of quantum materials simulations on distributed CPU-GPU systemsProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/2807591.2807654(1-12)Online publication date: 15-Nov-2015
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Kabir KHaidar ATomov SDongarra J(2015)Performance Analysis and Optimisation of Two-sided Factorization Algorithms for Heterogeneous PlatformProcedia Computer Science10.1016/j.procs.2015.05.22251:C(180-190)Online publication date: 1-Sep-2015
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Haidar AKurzak JLuszczek PGropp WMatsuoka S(2013)An improved parallel singular value algorithm and its implementation for multicore hardwareProceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis10.1145/2503210.2503292(1-12)Online publication date: 17-Nov-2013
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Haidar AGates MTomov SDongarra JMalony ANemirovsky MMidkiff S(2013)Toward a scalable multi-GPU eigensolver via compute-intensive kernels and efficient communicationProceedings of the 27th international ACM conference on International conference on supercomputing10.1145/2464996.2465438(223-232)Online publication date: 10-Jun-2013
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Van Zee Fvan de Geijn RQuintana-Ortí GElizondo G(2012)Families of Algorithms for Reducing a Matrix to Condensed FormACM Transactions on Mathematical Software10.1145/2382585.238258739:1(1-32)Online publication date: 1-Nov-2012
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Ballard GDemmel JKnight N(2012)Communication avoiding successive band reductionACM SIGPLAN Notices10.1145/2370036.214582247:8(35-44)Online publication date: 25-Feb-2012
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