The Drazin inverse of a singular,unreduced tridiagonal matrix

For a tridiagonal, singular matrix A   we present a method for the computation of the polynomial p(λ)$p(\lambda )$ such that A^D=p(A)$A^D=p(A)$ holds, where A^D$A^D$ is the Drazin inverse of A. The approach is based on the recursion of characteristic polynomials of leading principal submatrices of A.