IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i10p893-d270249.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/10/893/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/10/893/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Abdalla, Bahaaeldin & Abdeljawad, Thabet, 2019. "On the oscillation of Caputo fractional differential equations with Mittag–Leffler nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 173-177.
    3. Zhang, Xing & Jiang, Xiaoyu & Jiang, Zhaolin & Byun, Heejung, 2022. "An improvement of methods for solving the CUPL-Toeplitz linear system," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    4. Fu, Yaru & Jiang, Xiaoyu & Jiang, Zhaolin & Jhang, Seongtae, 2021. "Fast algorithms for finding the solution of CUPL-Toeplitz linear system from Markov chain," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    5. Jehad Alzabut & Velu Muthulakshmi & Abdullah Özbekler & Hakan Adıgüzel, 2019. "On the Oscillation of Non-Linear Fractional Difference Equations with Damping," Mathematics, MDPI, vol. 7(8), pages 1-14, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:893-:d:270249. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.