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Error bounds of Rayleigh–Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems

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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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Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Akira Imakura & Tetsuya Sakurai

  2. School of Mathematics Sciences, Dalian University of Technology, Dalian, 11024, China

    Lei Du

Authors
  1. Akira Imakura
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  2. Lei Du
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  3. Tetsuya Sakurai
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Corresponding author

Correspondence to Akira Imakura.

Additional information

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

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