A note on computing the inverse and the determinant of a pentadiagonal Toeplitz matrix

A fast and effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been recently proposed [E. Kilic, M. El-Mikkawy, A computational algorithm for special nth order pentadiagonal Toeplitz determinants, Appl. Math. Comput. 199 (2) (2008) 820–822]. The complexity of the algorithm is 11n − 17. In this paper, we present an algorithm with the cost of 9n+39n+3 for calculating the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered. Numerical examples are given to illustrate the effectiveness of our method.