Abstract
Recently, contour integral-based methods have been actively studied for solving interior eigenvalue problems that find all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we reconsider the algorithms of the five typical contour integral-based eigensolvers from the viewpoint of projection methods, and then map the relationships among these methods. From the analysis, we conclude that all contour integral-based eigensolvers can be regarded as projection methods and can be categorized based on their subspace used, the type of projection and the problem to which they are applied implicitly.
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Acknowledgements
The authors would like to thank Dr. Kensuke Aishima, The University of Tokyo for his valuable comments. The authors are also grateful to an anonymous referee for useful comments.
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This research was supported partly by Interdisciplinary Computational Science Program in CCS, University of Tsukuba, Strategic Programs for Innovative Research (SPIRE) Field 5 “The origin of matter and the universe”, JST/CREST and KAKENHI (Grant Nos. 25286097, 25870099), the Fundamental Research Funds for the Central Universities (No: DUT16LK05) and the National Natural Science Foundation of China (No: 11501079).
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Imakura, A., Du, L. & Sakurai, T. Relationships among contour integral-based methods for solving generalized eigenvalue problems. Japan J. Indust. Appl. Math. 33, 721–750 (2016). https://doi.org/10.1007/s13160-016-0224-x
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DOI: https://doi.org/10.1007/s13160-016-0224-x