Abstract
We investigate contour integral-based eigensolvers for computing all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we focus on a Rayleigh–Ritz type method and analyze its error bounds. From the results of our analysis, we conclude that the Rayleigh–Ritz type contour integral-based eigensolver with sufficient subspace size can achieve high accuracy for target eigenpairs even if some eigenvalues exist outside but near the region.
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This work was supported in part by MEXT SPIRE Field 5, JICFuS, JST/CREST and KAKENHI (Grant Nos. 25286097, 25870099).
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Imakura, A., Du, L. & Sakurai, T. Error bounds of Rayleigh–Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems. Numer Algor 71, 103–120 (2016). https://doi.org/10.1007/s11075-015-9987-4
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DOI: https://doi.org/10.1007/s11075-015-9987-4