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A parallel generalized conjugate gradient method for large scale eigenvalue problems

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Abstract

Based on damping blocked inverse power method, a type of generalized parallel conjugate gradient method is proposed for large scale eigenvalue problems. Techniques for orthogonalization and computing Rayleigh-Ritz problems are introduced to improve the stability, efficiency and scalability. Furthermore, a computing package is built based on the proposed method here. Some numerical tests are provided to validate the stability, efficiency and scalability of the method in this paper. The corresponding computing package can be downloaded from the web site:  https://github.com/pase2017/GCGE-1.0.

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  1. https://sparse.tamu.edu.

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Authors and Affiliations

  1. Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin, 300222, China

    Yu Li

  2. ICMSEC, LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Hehu Xie

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Hehu Xie

  4. CAEP Software Center for High Performance Numerical Simulation, No. 6, Huayuan Road, Haidian District, Beijing, 100088, China

    Ran Xu & Chun’guang You

  5. Institute of Electrical Engineering, Chinese Academy of Sciences, No. 6, Beiertiao, Zhongguancun, Haidian, Beijing, 100190, China

    Ning Zhang

Authors
  1. Yu Li
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  2. Hehu Xie
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  3. Ran Xu
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  4. Chun’guang You
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  5. Ning Zhang
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Corresponding author

Correspondence to Hehu Xie.

Additional information

This work was supported by Science Challenge Project (No. TZ2016002), National Natural Science Foundations of China (NSFC 11771434, 91730302), the National Center for Mathematics and Interdisciplinary Science, CAS.

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Li, Y., Xie, H., Xu, R. et al. A parallel generalized conjugate gradient method for large scale eigenvalue problems. CCF Trans. HPC 2, 111–122 (2020). https://doi.org/10.1007/s42514-020-00029-6

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  • DOI: https://doi.org/10.1007/s42514-020-00029-6

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