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Skew cyclic displacements and inversions of two innovative patterned Matrices

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  • Jiang, Xiaoyu
  • Hong, Kicheon

Abstract

In this paper, we deal mainly with a class of column upper-plus-lower (CUPL) Toeplitz matrices without Toeplitz structure, which are “close” to the Toeplitz matrices in the sense that their (−1,1)-cyclic displacements coincide with cyclic displacement of some Toeplitz matrices. By constructing the corresponding displacement of the matrices, we derive the formulas on representation of the inverses of the CUPL Toeplitz matrices in the form of sums of products of factor (1, 1)-circulants and (−1,−1)-circulants. Furthermore, through the relation between the CUPL Toeplitz matrices and the CUPL Hankel matrices, the inverses of the CUPL Hankel matrices can be obtained as well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:308:y:2017:i:c:p:174-184
    DOI: 10.1016/j.amc.2017.03.024
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    References listed on IDEAS

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    1. 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.
    2. Jiang, Xiaoyu & Hong, Kicheon, 2015. "Explicit inverse matrices of Tribonacci skew circulant type matrices," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 93-102.
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    Cited by:

    1. 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).
    2. 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).
    3. 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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