Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Online Fault Classification in HPC Systems Through Machine Learning Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Linear Systems Solvers for Distributed-Memory Machines with GPU Accelerators

Authors : Jakub Kurzak, Mark Gates, Ali Charara, Asim YarKhan, Ichitaro Yamazaki, Jack Dongarra

Published in: Euro-Par 2019: Parallel Processing

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This work presents two implementations of linear solvers for distributed-memory machines with GPU accelerators—one based on the Cholesky factorization and one based on the LU factorization with partial pivoting. The routines are developed as part of the Software for Linear Algebra Targeting Exascale (SLATE) package, which represents a sharp departure from the traditional conventions established by legacy packages, such as LAPACK and ScaLAPACK. The article lays out the principles of the new approach, discusses the implementation details, and presents the performance results.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Automatic Exploration of Reduced Floating-Point Representations in Iterative Methods
next chapter Radio-Astronomical Imaging: FPGAs vs GPUs
Footnotes
Literature
1.
Andersen, B.S., Gunnels, J.A., Gustavson, F., Wasniewski, J.: A recursive formulation of the inversion of symmetric positive definite matrices in packed storage data format. PARA 2, 287–296 (2002)MATH
2.
Andersen, B.S., Waśniewski, J., Gustavson, F.G.: A recursive formulation of Cholesky factorization of a matrix in packed storage. ACM Trans. Math. Softw. (TOMS) 27(2), 214–244 (2001)CrossRef
3.
Blackford, L.S., et al.: ScaLAPACK Users’ Guide. SIAM, Philadelphia (1997)CrossRef
4.
Castaldo, A., Whaley, C.: Scaling LAPACK panel operations using parallel cache assignment. In: ACM Sigplan Notices, vol. 45, pp. 223–232. ACM (2010)
5.
Chan, E., van de Geijn, R., Chapman, A.: Managing the complexity of lookahead for LU factorization with pivoting. In: Proceedings of the Twenty-second Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 200–208. ACM (2010)
6.
Choi, J., Dongarra, J., Ostrouchov, S., Petitet, A., Walker, D., Whaley, C.: Design and implementation of the ScaLAPACK LU, QR, and Cholesky factorization routines. Sci. Program. 5(3), 173–184 (1996)
7.
Dongarra, J., Faverge, M., Ltaief, H., Luszczek, P.: Achieving numerical accuracy and high performance using recursive tile LU factorization with partial pivoting. Concurr. Comput. Pract. Exp. 26(7), 1408–1431 (2014)CrossRef
8.
Gates, M., et al.: SLATE working note 2: C++ API for BLAS and LAPACK. Technical report ICL-UT-17-03, Innovative Computing Laboratory, University of Tennessee, June 2017. Revision 03–2018
9.
Gustavson, F., Henriksson, A., Jonsson, I., Kågström, B., Ling, P.: Recursive blocked data formats and BLAS’s for dense linear algebra algorithms. In: Kågström, B., Dongarra, J., Elmroth, E., Waśniewski, J. (eds.) PARA 1998. LNCS, vol. 1541, pp. 195–206. Springer, Heidelberg (1998). https://​doi.​org/​10.​1007/​BFb0095337CrossRef
10.
Gustavson, F., Karlsson, L., Kågström, B.: Parallel and cache-efficient in-place matrix storage format conversion. ACM Trans. Math. Softw. (TOMS) 38(3), 17 (2012)CrossRef
11.
12.
Sala, K., Teruel, X., Perez, J.M., Peña, A.J., Beltran, V., Labarta, J.: Integrating blocking and non-blocking MPI primitives with task-based programming models. Parallel Comput. 85, 153–166 (2019)CrossRef
13.
Sorin, D.J., Hill, M.D., Wood, D.A.: A primer on memory consistency and cache coherence. Synth. Lect. Comput. Arch. 6(3), 1–212 (2011)
14.
Strazdins, P., et al.: A comparison of lookahead and algorithmic blocking techniques for parallel matrix factorization (1998)
15.
Sukkari, D., Ltaief, H., Keyes, D.: A high performance QDWH-SVD solver using hardware accelerators. ACM Trans. Math. Softw. (TOMS) 43(1), 6 (2016)MathSciNetCrossRef
Metadata
Title
Linear Systems Solvers for Distributed-Memory Machines with GPU Accelerators
Authors
Jakub Kurzak
Mark Gates
Ali Charara
Asim YarKhan
Ichitaro Yamazaki
Jack Dongarra
Copyright Year
2019
Book
Euro-Par 2019: Parallel Processing

Print ISBN: 978-3-030-29399-4

Electronic ISBN: 978-3-030-29400-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-29400-7_35

Premium Partner

    Image Credits