The stability of inversion formulas for Toeplitz matrices

AbstractIt is shown that under suitable assumptions the well-known formulas for the inverse of Toeplitz matrices that are due to Gohberg and Semencul and Heinig are weakly stable, i.e., they are numerically forward stable if the matrices that are by assumption nonsingular are actually well conditioned. The same is true for another, less-known pair of inversion formulas that only involve the left biorthogonal Szegö polynomials