On determinants of cyclic pentadiagonal matrices with Toeplitz structure. (15th January 2017)

• Record Type: Journal Article
• Authors: Jia, Jiteng; Li, Sumei
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 2(2017)
• Page Start: 304
• Page End: 309
• Publication Date: 2017-01-15
• Subjects: Cyclic pentadiagonal matrix -- Toeplitz matrix -- Block matrix -- Triangular transformation -- Computational cost; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.11.031
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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 n -by- n 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 ) is derived for computing n th order cyclic pentadiagonal Toeplitz determinants. Some numerical experiments are given to show the performance of the proposed algorithm.