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A Modified Inverse Iteration Method for Computing the Symmetric Tridiagonal Eigenvectors

Author

Listed:
  • Wei Chu

    (School of Naval Architecture and Ocean Engineering, Huazhong University of Sciences and Technology, Wuhan 430074, China)

  • Yao Zhao

    (School of Naval Architecture and Ocean Engineering, Huazhong University of Sciences and Technology, Wuhan 430074, China
    Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics (HUST), Wuhan 430074, China)

  • Hua Yuan

    (School of Naval Architecture and Ocean Engineering, Huazhong University of Sciences and Technology, Wuhan 430074, China
    Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics (HUST), Wuhan 430074, China)

Abstract

This paper presents a novel method for computing the symmetric tridiagonal eigenvectors, which is the modification of the widely used Inverse Iteration method. We construct the corresponding algorithm by a new one-step iteration method, a new reorthogonalization method with the general Q iteration and a significant modification when calculating severely clustered eigenvectors. The numerical results show that this method is competitive with other existing methods, especially when computing part eigenvectors or severely clustered ones.

Suggested Citation

  • Wei Chu & Yao Zhao & Hua Yuan, 2022. "A Modified Inverse Iteration Method for Computing the Symmetric Tridiagonal Eigenvectors," Mathematics, MDPI, vol. 10(19), pages 1-29, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3636-:d:933657
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    References listed on IDEAS

    as
    1. Wei Chu & Yao Zhao & Hua Yuan, 2022. "A Novel Divisional Bisection Method for the Symmetric Tridiagonal Eigenvalue Problem," Mathematics, MDPI, vol. 10(15), pages 1-22, August.
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