The stability of formulae of the Gohberg-Semencul-Trench type for Moore-Penrose and group inverses of Toeplitz matrices

We present a stability analysis of Gohberg-Semencul-Trench type formulae for the Moore-Penrose and group inverses of singular Toeplitz matrices. We develop a fast algorithm for the computation of the Moore-Penrose inverse based on a Gohberg-Semencul-Trench type formula and the LSQR method. For the group inverse, the DGMRES method is used to perform the fast computation. Numerical tests show that the fast algorithms designed here are at least as good as the known Newton iteration.