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On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems

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Abstract

In a recent work (J. Sci. Comput. 85 (2020), no. 3), the author generalized the Chebyshev-Davidson method appeared in standard eigenvalue problems to symmetric generalized eigenvalue problems. The theoretical derivation indicates that the Chebyshev-Davidson method for symmetric generalized eigenvalue problems only admits local convergence; thus, in this paper, we adopt a flexible strategy to improve the global convergence and to save number of iteration steps. Moreover, the deflation technique used for computing several eigenpairs in the proposed Chebyshev-Davidson method cannot be implemented in parallel; therefore, we construct a flexible block Chebyshev-Davidson method for computing several eigenpairs of symmetric generalized eigenvalue problems. The block implementation is important in scientific computing since it allows parallelism and efficient use of local memory. Numerical experiments are carried out to show great superiority and robustness over some state-of-the-art iteration methods.

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Acknowledgements

The authors are very much indebted to the referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of this paper.

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Authors and Affiliations

  1. Hunan Key Laboratory of Analytical Mathematics and Applications, School of Mathematics and Statistics, Central South University, Changsha, 410083, People’s Republic of China

    Cun-Qiang Miao

  2. School of Mathematics and Statistics, Hunan First Normal University, Changsha, 410205, People’s Republic of China

    Lan Cheng

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  1. Cun-Qiang Miao
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  2. Lan Cheng
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Correspondence to Lan Cheng.

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Communicated by: Peter Benner

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Supported by the National Natural Science Foundation of China (No. 11901361 and No. 12001048) and the Natural Science Foundation of Hunan Province (No. 2021JJ40708), P.R. China.

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Miao, CQ., Cheng, L. On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems. Adv Comput Math 49, 78 (2023). https://doi.org/10.1007/s10444-023-10078-4

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  • DOI: https://doi.org/10.1007/s10444-023-10078-4

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