A new recursive algorithm for inverting general periodic pentadiagonal and anti-pentadiagonal matrices

In the current article, the authors present a new recursive symbolic computational algorithm, that will never break down, for inverting general periodic pentadiagonal and anti-pentadiagonal matrices. It is a natural generalization of the work presented in [M.E.A. El-Mikkawy, E.D. Rahmo, A new recursive algorithm for inverting general tridiagonal and anti-tridiagonal matrices, Appl. Math. Comput. 204 (2008) 368–372]. The algorithm is suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. An illustrative example is given.