On determinants of cyclic pentadiagonal matrices with Toeplitz structure. (15th January 2017) - Jia, Jiteng; Li, Sumei
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.