ON INVERSES AND EIGENPAIRS OF PERIODIC TRIDIAGONAL TOEPLITZ MATRICES WITH PERTURBED CORNERS

Yunlan Wei; Xiaoyu Jiang; Zhaolin Jiang; Sugoog Shon

doi:10.11948/20190105

2020 Volume 10 Issue 1

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Yunlan Wei, Xiaoyu Jiang, Zhaolin Jiang, Sugoog Shon. ON INVERSES AND EIGENPAIRS OF PERIODIC TRIDIAGONAL TOEPLITZ MATRICES WITH PERTURBED CORNERS[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 178-191. doi: 10.11948/20190105

Citation:

Yunlan Wei, Xiaoyu Jiang, Zhaolin Jiang, Sugoog Shon. ON INVERSES AND EIGENPAIRS OF PERIODIC TRIDIAGONAL TOEPLITZ MATRICES WITH PERTURBED CORNERS[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 178-191. doi: 10.11948/20190105

ON INVERSES AND EIGENPAIRS OF PERIODIC TRIDIAGONAL TOEPLITZ MATRICES WITH PERTURBED CORNERS

1.
School of Mathematics and Statistics, Linyi University, Linyi, 276000, China
2.
College of Information Technology, The University of Suwon, Hwaseong-si, 445-743, Korea
3.
School of Information Science and Technology, Linyi University, Linyi, 276000, China

Corresponding authors: Email address: jxy19890422@sina.com(X. Jiang); Email address: jzh1208@sina.com(Z. Jiang)
Fund Project: The research was supported by Natural Science Foundation of Shandong Province (No. ZR2016AM14), National Natural Science Foundation of China (No. 11671187) and the PhD Research Foundation of Linyi University (No. LYDX2018BS052)

Abstract

Abstract

In this paper, we derive explicit determinants, inverses and eigenpairs of periodic tridiagonal Toeplitz matrices with perturbed corners of Type $I$. The Mersenne numbers play an important role in these explicit formulas derived. Our main approaches include clever uses of the Schur complement and matrix decomposition with the Sherman-Morrison-Woodbury formula. Besides, the properties of Type $II$ matrix can be also obtained, which benefits from the relation between Type $I$ and $II$ matrices. Lastly, we give three algorithms for these basic quantities and analyze them to illustrate our theoretical results.
- Determinant /
- inverse /
- eigenpair /
- periodic tridiagonal Toeplitz matrix
MSC: 15A09, 15A15, 15A69, 65F05

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References

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