An efficient numerical algorithm for the determinant of a cyclic pentadiagonal Toeplitz matrix

In the past few years, a number of numerical and symbolic algorithms for evaluating the determinants of cyclic pentadiagonal matrices have been developed. In this paper, we present a fast numerical algorithm for the determinant of an n-by-n cyclic pentadiagonal matrix with Toeplitz structure. The algorithm is based upon a certain type of matrix reordering and partitioning, and linear transformation. Some numerical examples are provided, and the results are compared with the ones obtained via Matlab built-in function and two existing algorithms. All of the numerical experiments are performed on a computer with the aid of programs written in Matlab.