On inverses of pentadiagonal matrices

In this work, we introduce an algorithm that computes the inverse of a general nonsingular pentadiagonal matrix. This is done by computing the entries of the Crout's LU factorization of the matrix, then recursive relations are set up and used to compute the inverses of L and U, where these entries are filled up starting with the main diagonal, and then the first and second immediate upper diagonals in U-1. The same process is done for L-1, where the main diagonal is computed first, then the first and second immediate lower diagonals respectively. Finally, the required inverse is set to be equal to U-1L-1.