In this paper, the inverse of a sevendiagonal (anti-sevendiagonal) matrix is investigated by employing the special structure and the LU decompositions of the sevendiagonal matrix. We present a new recursive algorithm for inverting general periodic sevendiagonal and anti-sevendiagonal matrices. The algorithm is suited for implementation using computer algebra systems (CAS) such as Mathematics, Macsyma, Matlab and Maple. The effectiveness of the approach is demonstrated by a numerical example.

periodic sevendiagonal matrix, periodic anti-sevendiagonal matrix, LU factorization, inverse matrix, recursive algorithm, computer algebra systems.