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Properties of a class of perturbed Toeplitz periodic tridiagonal matrices

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Abstract

In this paper, for a class of perturbed Toeplitz periodic tridiagonal (PTPT) matrices, some properties, including the determinant, the inverse matrix, the eigenvalues and the eigenvectors, are studied in detail. Specifically, the determinant of the PTPT matrix can be explicitly expressed using the well-known Fibonacci numbers; the inverse of the PTPT matrix can also be explicitly expressed using the Lucas number and only four elements in the PTPT matrix. Eigenvalues and eigenvectors can be obtained under certain conditions. In addition, some algorithms are presented based on these theoretical results. Comparison of our new algorithms and some recent works is given. Numerical results confirm our new theoretical results and show that the new algorithms not only can obtain accurate results but also have much better computing efficiency than some existing algorithms studied recently.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, Linyi, 276000, China

    Yaru Fu, Xiaoyu Jiang & Zhaolin Jiang

  2. College of Information Technology, The University of Suwon, Hwaseong-si, 445-743, South Korea

    Yaru Fu & Seongtae Jhang

  3. School of Information Science and Technology, Linyi University, Linyi, 276000, China

    Xiaoyu Jiang

Authors
  1. Yaru Fu
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  2. Xiaoyu Jiang
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  3. Zhaolin Jiang
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  4. Seongtae Jhang
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Correspondence to Xiaoyu Jiang or Zhaolin Jiang.

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Communicated by Yimin wei.

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The research was supported by National Natural Science Foundation of China (Grant No.11671187) and the PhD Research Foundation of Linyi University (Grant No. LYDX2018BS052).

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Fu, Y., Jiang, X., Jiang, Z. et al. Properties of a class of perturbed Toeplitz periodic tridiagonal matrices. Comp. Appl. Math. 39, 146 (2020). https://doi.org/10.1007/s40314-020-01171-1

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  • DOI: https://doi.org/10.1007/s40314-020-01171-1

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