文章基本信息

标题：Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices
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作者：Yunlan Wei ; Xiaoyu Jiang ; Zhaolin Jiang 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-11
DOI：10.1186/s13662-019-2335-6
出版社：Hindawi Publishing Corporation
摘要：In this paper, we deal mainly with a class of periodic tridiagonal Toeplitz matrices with perturbed corners. By matrix decomposition with the Sherman–Morrison–Woodbury formula and constructing the corresponding displacement of matrices we derive the formulas on representation of the determinants and inverses of the periodic tridiagonal Toeplitz matrices with perturbed corners of type I in the form of products of Fermat numbers and some initial values. Furthermore, the properties of type II matrix can be also obtained, which benefits from the relation between type I and II matrices. Finally, we propose two algorithms for computing these properties and make some analysis about them to illustrate our theoretical results.
关键词：15A09;15A15;65F40;Determinant;Inverse;Fermat number;Periodic tridiagonal Toeplitz matrix;Sherman;Morrison;Woodbury formula