A fast and reliable algorithm for evaluating nth order pentadiagonal determinants

In the current article we present a fast and reliable algorithm for evaluating nth order pentadiagonal determinants in linear time. It is a natural generalization of the DETGTRI algorithm [M. El-Mikkawy, A fast algorithm for evaluating nth order tri-diagonal determinants, J. Comput. Appl. Math. 166 (2004) 581–584]. The algorithm is suited for implementation using computer algebra systems (CAS) such as MACSYMA and MAPLE. Some illustrative examples are given.