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Fast tridiagonal solvers on the GPU

Authors:

Jonathan Cohen,

John D. OwensAuthors Info & Claims

ACM SIGPLAN Notices, Volume 45, Issue 5

Pages 127 - 136

https://doi.org/10.1145/1837853.1693472

Published: 09 January 2010 Publication History

Abstract

We study the performance of three parallel algorithms and their hybrid variants for solving tridiagonal linear systems on a GPU: cyclic reduction (CR), parallel cyclic reduction (PCR) and recursive doubling (RD). We develop an approach to measure, analyze, and optimize the performance of GPU programs in terms of memory access, computation, and control overhead. We find that CR enjoys linear algorithm complexity but suffers from more algorithmic steps and bank conflicts, while PCR and RD have fewer algorithmic steps but do more work each step. To combine the benefits of the basic algorithms, we propose hybrid CR+PCR and CR+RD algorithms, which improve the performance of PCR, RD and CR by 21%, 31% and 61% respectively. Our GPU solvers achieve up to a 28x speedup over a sequential LAPACK solver, and a 12x speedup over a multi-threaded CPU solver.

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Cen RRen B(2025)Layer-Based Simulation for Three-Dimensional Fluid Flow in Spherical CoordinatesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.336052131:2(1435-1447)Online publication date: Feb-2025
https://doi.org/10.1109/TVCG.2024.3360521
Liu KXue W(2023)A Novel Compute-Efficient Tridiagonal Solver for Many-Core ArchitecturesIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2022.321476234:1(195-206)Online publication date: 1-Jan-2023
https://doi.org/10.1109/TPDS.2022.3214762
Wang ZJuhasz Z(2023)Efficient GPU implementation of the multivariate empirical mode decomposition algorithmJournal of Computational Science10.1016/j.jocs.2023.10218074(102180)Online publication date: Dec-2023
https://doi.org/10.1016/j.jocs.2023.102180
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Index Terms

Fast tridiagonal solvers on the GPU
1. Computing methodologies
  1. Parallel computing methodologies
    1. Parallel programming languages
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Parallel programming languages

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Information & Contributors

Information

Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 45, Issue 5

PPoPP '10

May 2010

346 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/1837853

Issue’s Table of Contents

PPoPP '10: Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming
January 2010
372 pages
ISBN:9781605588773
DOI:10.1145/1693453
General Chairs:
R. Govindarajan
Indian Institute of Science
,
David Padua
UIUC
,
Program Chair:
Mary Hall
University of Utah

Copyright © 2010 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 January 2010

Published in SIGPLAN Volume 45, Issue 5

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https://doi.org/10.1109/TVCG.2024.3360521
Liu KXue W(2023)A Novel Compute-Efficient Tridiagonal Solver for Many-Core ArchitecturesIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2022.321476234:1(195-206)Online publication date: 1-Jan-2023
https://doi.org/10.1109/TPDS.2022.3214762
Wang ZJuhasz Z(2023)Efficient GPU implementation of the multivariate empirical mode decomposition algorithmJournal of Computational Science10.1016/j.jocs.2023.10218074(102180)Online publication date: Dec-2023
https://doi.org/10.1016/j.jocs.2023.102180
Lutsyshyn YNavarrete FBauer D(2023)The N-shaped partition method: A novel parallel implementation of the Crank Nicolson algorithmComputer Physics Communications10.1016/j.cpc.2023.108713287(108713)Online publication date: Jun-2023
https://doi.org/10.1016/j.cpc.2023.108713
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Tsai YLuszczek PDongarra J(2022) Mixed-Precision Algorithm for Finding Selected Eigenvalues and Eigenvectors of Symmetric and Hermitian Matrices 1 2022 IEEE/ACM Workshop on Latest Advances in Scalable Algorithms for Large-Scale Heterogeneous Systems (ScalAH)10.1109/ScalAH56622.2022.00011(43-50)Online publication date: Nov-2022
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