Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing

We present a Hessenberg reduction (HR) algorithm for hybrid systems of homogeneous multicore with GPU accelerators that can exceed 25× the performance of the corresponding LAPACK algorithm running on current homogeneous multicores. This enormous acceleration is due to proper matching of algorithmic...

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Bibliographic Details
Published in:Parallel computing Vol. 36; no. 12; pp. 645 - 654
Main Authors: Tomov, Stanimire, Nath, Rajib, Dongarra, Jack
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2010
Subjects:
Accelerators
Algorithms
Bidiagonalization
Computation
Computer programs
Dense linear algebra
Eigenvalues
GPUs
Hessenberg reduction
Hybrid computing
Hybrid systems
Reduction
Running
Tridiagonalization
Two-sided factorizations
Hybrid computing
Bidiagonalization
GPUs
Tridiagonalization
Two-sided factorizations
Hessenberg reduction
Dense linear algebra
ISSN:0167-8191, 1872-7336
Online Access:Get full text
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Summary:We present a Hessenberg reduction (HR) algorithm for hybrid systems of homogeneous multicore with GPU accelerators that can exceed 25× the performance of the corresponding LAPACK algorithm running on current homogeneous multicores. This enormous acceleration is due to proper matching of algorithmic requirements to architectural strengths of the system’s hybrid components. The results described in this paper are significant because the HR has not been properly accelerated before on homogeneous multicore architectures, and it plays a significant role in solving non-symmetric eigenvalue problems. Moreover, the ideas from the hybrid HR are used to develop a hybrid tridiagonal reduction algorithm (for symmetric eigenvalue problems) and a bidiagonal reduction algorithm (for singular value decomposition problems). Our approach demonstrates a methodology that streamlines the development of a large and important class of algorithms on modern computer architectures of multicore and GPUs. The new algorithms can be directly used in the software stack that relies on LAPACK.
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ISSN:0167-8191
1872-7336
DOI:10.1016/j.parco.2010.06.001