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The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows

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Abstract

The explicit determinants, inverses and eigenpairs of periodic tridiagonal Toeplitz-like matrices with perturbed rows are presented in this paper. We derive the representation of the determinants and inverses in the form of products of Mersenne numbers and some initial values from matrix transformations, which reduces the computational complexity to a certain extent. Futhermore, we make some analysis about these basic quantities to illustrate our theoretical results.

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Acknowledgements

The research was supported by National Natural Science Foundation of China (Nos. 12001257 and 11671187), and the Ph.D. Research Foundation of Linyi University (Grant No. LYDX2018BS052).

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Authors and Affiliations

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

    Yunlan Wei & Zhaolin Jiang

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

    Yunlan Wei & Sugoog Shon

  3. School of Automation and Electrical Engineering, Linyi University, China, 276000, China

    Yanpeng Zheng

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  1. Yunlan Wei
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  2. Yanpeng Zheng
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  4. Sugoog Shon
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Correspondence to Yanpeng Zheng or Zhaolin Jiang.

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Wei, Y., Zheng, Y., Jiang, Z. et al. The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows. J. Appl. Math. Comput. 68, 623–636 (2022). https://doi.org/10.1007/s12190-021-01532-x

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  • DOI: https://doi.org/10.1007/s12190-021-01532-x

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