Abstract
In recent years, a numerical quadrature-based sparse eigensolver—the so-called Sakurai–Sugiura method—and its variants have attracted attention because of their highly coarse-grained parallelism. In this paper, we propose a memory-saving technique for a variant of the Sakurai–Sugiura method. The proposed technique can be utilized when inner linear systems are solved with the shifted block conjugate gradient method. Using our technique, eigenvalues and residual norms can be obtained without the explicit need to compute the eigenvector. This technique saves a considerable amount of memory space when eigenvectors are unnecessary. Our technique is also beneficial in cases where eigenvectors are necessary, because the residual norms of the target eigenpairs can be cheaply computed and monitored during each iteration step of the inner linear solver.
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Acknowledgements
The authors would like to thank Dr. Noritaka Shimizu for giving us a matrix derived from a nuclear shell-model. The authors wish to thank Dr. Jun-Ichi Iwata for giving us a matrix derived from a real-space density functional calculation. The authors are grateful to Dr. Hiroshi Ohno for his valuable comments and for providing us a matrix from quantum chromodynamics. The authors would like to thank the anonymous reviewers for their helpful comments and suggestions. This work was supported in part by JST/CREST and MEXT KAKENHI (Grant Nos. 25104701, 25286097).
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Futamura, Y., Sakurai, T. (2017). Memory-Saving Technique for the Sakurai–Sugiura Eigenvalue Solver Using the Shifted Block Conjugate Gradient Method. In: Sakurai, T., Zhang, SL., Imamura, T., Yamamoto, Y., Kuramashi, Y., Hoshi, T. (eds) Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing. EPASA 2015. Lecture Notes in Computational Science and Engineering, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-62426-6_13
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DOI: https://doi.org/10.1007/978-3-319-62426-6_13
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