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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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Correspondence to Hehu Xie.

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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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