A structure-preserving algorithm for linear systems with circulant pentadiagonal coefficient matrices

Kong, Qiongxiang; Jia, Jinping

doi:10.1007/s10910-015-0509-3

Cited by 4 publications

(1 citation statement)

References 28 publications

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“…It is worth mentioning that circulant and skew circulant matrices play a crucial role in chemistry [15,18] and PDEs [5,22,26,27,33]. Circulant matrix not only was originally designed for fractional Brownian motion but also the sampling algorithm for the random fluctuating force [19].…”

Section: Introductionmentioning

confidence: 99%

On determinants, inverses, norms, and spread of skew circulant matrices involving the product of Pell and Pell-Lucas numbers

Fan¹,

Wei²,

Zheng³

et al. 2023

J. Math. Computer Sci.

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In this paper, we discuss skew circulant matrices involving the product of Pell and Pell-Lucas numbers. The invertibility of the skew circulant matrices is investigated, while the fundamental theorems on the determinants and inverses of such matrices are derived by simple construction matrices. Specifically, the determinant and inverse of n × n skew circulant matrices can be expressed by the (n − 1)th, nth, (n + 1)th, (n + 2)th product of Pell and Pell-Lucas numbers. Some norms and bounds for spread of these matrices are given, respectively. In addition, we generalized these results to skew left circulant matrix involving the product of Pell and Pell-Lucas numbers. Finally, several numerical examples are illustrated to show the effectiveness of our theoretical results.

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