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

Yunlan Wei | Zendy; Xiaoyu Jiang | Zendy; Zhaolin Jiang | Zendy; Sugoog Shon | Zendy

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

Author(s) -

Yunlan Wei,

Xiaoyu Jiang,

Zhaolin Jiang,

Sugoog Shon

Publication year - 2020

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20190105

Subject(s) - toeplitz matrix , tridiagonal matrix , mathematics , schur complement , mersenne prime , pure mathematics , matrix (chemical analysis) , algebra over a field , type (biology) , combinatorics , eigenvalues and eigenvectors , physics , quantum mechanics , ecology , materials science , composite material , biology

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.

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