Some results on determinants and inverses of nonsingular pentadiagonal matrices

A block matrix analysis is proposed to justify, and modify, a known algorithm for computing in O(n) time the determinant of a nonsingular n×n pentadiagonal matrix (n≥6) having nonzero entries on its second subdiagonal. Also, we describe a procedure for computing the inverse matrix with acceptable accuracy in O(n2) time. In the general nonsingular case, for n≥5, proper decompositions of the pentadiagonal matrix, as a product of two structured matrices, allow us to obtain both the determinant and the inverse matrix by exploiting low rank structures.