INVERSES AND EIGENPAIRS OF TRIDIAGONAL TOEPLITZ MATRIX WITH OPPOSITE-BORDERED ROWS | Zendy

Yaru Fu | Zendy; Xiaoyu Jiang | Zendy; Zhaolin Jiang | Zendy; Seong Tae Jhang | Zendy

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INVERSES AND EIGENPAIRS OF TRIDIAGONAL TOEPLITZ MATRIX WITH OPPOSITE-BORDERED ROWS

Author(s) -

Yaru Fu,

Xiaoyu Jiang,

Zhaolin Jiang,

Seong Tae Jhang

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 - 10.11948/20190287

Subject(s) - tridiagonal matrix , toeplitz matrix , row , mathematics , eigenvalues and eigenvectors , matrix (chemical analysis) , fibonacci number , pure mathematics , combinatorics , computer science , physics , quantum mechanics , materials science , database , composite material

In this paper, tridiagonal Toeplitz matrix (type I, type II) with opposite-bordered rows are introduced. Main attention is paid to calculate the determinants, the inverses and the eigenpairs of these matrices. Specifically, the determinants of an n× n tridiagonal Toeplitz matrix with oppositebordered rows can be explicitly expressed by using the (n−1)th Fibonacci number, the inversion of the tridiagonal Toeplitz matrix with opposite-bordered rows can also be explicitly expressed by using the Fibonacci numbers and unknown entries from the new matrix. Besides, we give the expression of eigenvalues and eigenvectors of the tridiagonal Toeplitz matrix with oppositebordered rows. In addition, some algorithms are presented based on these theoretical results. Numerical results show that the new algorithms have much better computing efficiency than some existing algorithms studied recently.

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