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A Novel Divisional Bisection Method for the Symmetric Tridiagonal Eigenvalue Problem

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

The embarrassingly parallel nature of the Bisection Algorithm makes it easy and efficient to program on a parallel computer, but with an expensive time cost when all symmetric tridiagonal eigenvalues are wanted. In addition, few methods can calculate a single eigenvalue in parallel for now, especially in a specific order. This paper solves the issue with a new approach that can parallelize the Bisection iteration. Some pseudocodes and numerical results are presented. It shows our algorithm reduces the time cost by more than 35–70% compared to the Bisection algorithm while maintaining its accuracy and flexibility.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2782-:d:881464
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    References listed on IDEAS

    as
    1. Salud Bartoll & Ronald Richard Jiménez-Munguía & Rubén Alejandro Martínez-Avendaño & Alfred Peris, 2022. "Chaos for the Dynamics of Toeplitz Operators," Mathematics, MDPI, vol. 10(3), pages 1-14, January.
    2. Yunlan Wei & Yanpeng Zheng & Zhaolin Jiang & Sugoog Shon, 2019. "A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers," Mathematics, MDPI, vol. 7(10), pages 1-11, September.
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    Cited by:

    1. 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.

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