A Gohberg-Semencul Type Formula for the Inverse of Conjugate-Toeplitz Matrix and Applications

Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our Gohberg-Semencul type formula leads to an efficient way to solve the conjugate-Toeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugate-Hankel matrix is also considered.