A new Toeplitz inversion formula, stability analysis and the value

In this paper, Toeplitz and Hankel inversion formulae are presented by the idea of skew cyclic displacement. A new Toeplitz inversion formula can be denoted as a sum of products of skew circulant matrices and upper triangular Toeplitz matrices. A new Hankel inversion formula can be denoted as a sum of products of skew left circulant matrices and upper triangular Toeplitz matrices. The stability of their inverse formulae are discussed and their algorithms are given respectively. How the analogue of our formulae lead to a more efficient way to solve the Toeplitz and Hankel linear system of equations are proposed.