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GPU Solutions to Multi-scale Problems in Science and Engineering pp 543–554Cite as

Implementations of Main Algorithms for Generalized Symmetric Eigenproblem on GPU Accelerator

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Part of the book series: Lecture Notes in Earth System Sciences ((LNESS))

Abstract

To solve a generalized eigensystem problem, we firstly need to transform the generalized eigenproblem to a standard eigenproblem, and then reduce a matrix to tridiagonal form. These are based on both blocked Cholesky decomposition and blocked Householder tridiagonalization method. We present parallel implementations of standard transformation which combines the Cholesky into the transformation from generalized to standard form, and reduction of a dense matrix to tridiagonal form on GPU accelerator using CUBLAS. Experimental results clearly demonstrate the potential of data-parallel coprocessors for scientific computations. When comparing against the CPU implementation, the GPU implementations achieve above 16-fold and 20-fold speedups in double precision respectively.

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Acknowledgments

This work is supported by the National Science Foundation of China (Grant No. 60873113) and 863 Program (2009AA01A134, 2010AA012301).

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Authors and Affiliations

  1. Supercomputing Center, Computer Network Information Center, Chinese Academy of Sciences, 100190 , Beijing, China

    Yonghua Zhao, Fang Liu, Yangang Wang & Xuebin Chi

Authors
  1. Yonghua Zhao
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  2. Fang Liu
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  3. Yangang Wang
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  4. Xuebin Chi
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Corresponding author

Correspondence to Yonghua Zhao .

Editor information

Editors and Affiliations

  1. University of Minnesota, Dep. of Earth Sciences and Minnesota, Supercomputing Institute, Pillsbury Hall 23, Minneapolis, 55455, Minnesota, USA

    David A. Yuen

  2. Network Information Center, Comuter Center and Computer, Zhong Guan Cun 4, Beijing, 100190, China, People's Republic

    Long Wang

  3. Supercomputing Center, Zhong Guan Cun 4, Beijing, 100190, China, People's Republic

    Xuebin Chi

  4. , Computer Science, University of Houston, Calhoun Street 4800, Houston, 77204, Texas, USA

    Lennart Johnsson

  5. Inst. Process Engineering (IPE), Chinese Academy of Sciences, Zhongguancun North Second Street 1, Beijing, 100190, China, People's Republic

    Wei Ge

  6. , Laboratory of Computational Geodynamics,, Chinese Academy of Sciences, Yu Quan Lu 19a, Beijing, 100049, China, People's Republic

    Yaolin Shi

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Zhao, Y., Liu, F., Wang, Y., Chi, X. (2013). Implementations of Main Algorithms for Generalized Symmetric Eigenproblem on GPU Accelerator. In: Yuen, D., Wang, L., Chi, X., Johnsson, L., Ge, W., Shi, Y. (eds) GPU Solutions to Multi-scale Problems in Science and Engineering. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16405-7_33

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