On determinants of cyclic pentadiagonal matrices with Toeplitz structure

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• 作者：Jiteng Jia<sup>asup><sup> ; sup><sup>lavenderjjt@163.comsup> ; Sumei Li<sup>bsup>
• 关键词：Cyclic pentadiagonal matrix ; Toeplitz matrix ; Block matrix ; Triangular transformation ; Computational cost
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：73
• 期：2
• 页码：304-309
• 全文大小：351 K
• 卷排序：73

文摘

Cyclic pentadiagonal matrices with Toeplitz structure have received tremendous attention in recent years. In the current paper, we present a block upper triangular transformation of the cyclic pentadiagonal Toeplitz matrices. By using the transformation, the determinant of an nn-by-nn cyclic pentadiagonal Toeplitz matrix can be readily evaluated since one just needs to compute the determinant of a 4-by-4 matrix obtained from the transformation. In addition, an efficient numerical algorithm of O(n)O(n) is derived for computing nnth order cyclic pentadiagonal Toeplitz determinants. Some numerical experiments are given to show the performance of the proposed algorithm.