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A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

Author

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  • Yunlan Wei

    (School of Mathematics and Statistics, Linyi University, Linyi 276000, China
    College of Information Technology, The University of Suwon, Hwaseong-si 445-743, Korea)

  • Yanpeng Zheng

    (School of Mathematics and Statistics, Linyi University, Linyi 276000, China
    School of Automation and Electrical Engineering, Linyi University, Linyi 276000, China)

  • Zhaolin Jiang

    (School of Mathematics and Statistics, Linyi University, Linyi 276000, China)

  • Sugoog Shon

    (College of Information Technology, The University of Suwon, Hwaseong-si 445-743, Korea)

Abstract

In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit determinants and inverses of these matrices. One feature of these formulas is the connection with the famous Mersenne numbers. We also propose two algorithms to illustrate our formulas.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:893-:d:270249
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    References listed on IDEAS

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    1. da Fonseca, Carlos M. & Yılmaz, Fatih, 2015. "Some comments on k-tridiagonal matrices: Determinant, spectra, and inversion," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 644-647.
    2. Jiang, Zhao-lin & Wang, Dan-dan, 2016. "Explicit group inverse of an innovative patterned matrix," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 220-228.
    3. Jiang, Xiaoyu & Hong, Kicheon, 2017. "Skew cyclic displacements and inversions of two innovative patterned Matrices," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 174-184.
    4. Bin Zheng & Qinghua Feng, 2013. "Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
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    Cited by:

    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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