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Enhanced Error Estimates for Augmented Subspace Method

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Abstract

In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. For the first time, we strictly prove that the augmented subspace methods have the second order convergence rate between the two iteration steps, which is better than the existing theoretical results in Lin and Xie (Math Comp 84:71–88, 2015), Xie et al. (SIAM J Numer Anal 57(6):2519–2550, 2019), Xu et al. (SIAM J Sci Comput 42(5):A2655–A2677, 2020) and more consistent with the results of actual numerical test. These sharper estimates explicitly depict the dependence of convergence rate on the coarse spaces, which provides new advantages for the augmented subspace methods. Some numerical examples are finally presented to validate these new estimate results and the efficiency of our algorithms.

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Data sharing is not applicable to this paper as no datasets were generated or analysed during the current study.

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Acknowledgements

The authors would like to thank the editor and two anonymous referees for their valuable comments which improve this manuscript a lot.

Funding

This work was partly supported by the National Key Research and Development Program of China (2019YFA0709601), Beijing Natural Science Foundation (Z200003), National Natural Science Foundation of China (NSFC 11771434), the National Center for Mathematics and Interdisciplinary Science, CAS, and by the Research Foundation for Beijing University of Technology New Faculty (006000514122516).

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Authors and Affiliations

  1. China Electronics Technology Group Corporation No. 15 Research Institute, Beijing, 100083, China

    Haikun Dang

  2. LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No.55, Zhongguancun Donglu, Beijing, 100190, China

    Haikun Dang, Yifan Wang & Hehu Xie

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

    Haikun Dang, Yifan Wang & Hehu Xie

  4. Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Chenguang Zhou

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

    Chenguang Zhou

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  1. Haikun Dang
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  2. Yifan Wang
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  3. Hehu Xie
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  4. Chenguang Zhou
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Correspondence to Chenguang Zhou.

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Dang, H., Wang, Y., Xie, H. et al. Enhanced Error Estimates for Augmented Subspace Method. J Sci Comput 94, 40 (2023). https://doi.org/10.1007/s10915-022-02090-5

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