Inversion formulas for Toeplitz-plus-Hankel matrices.

The main aim of the present paper is to establish inversion formulas of Gohberg-Semencul type for Toeplitz-plus-Hankel matrices. In particular, it is shown how the inverse of such a structured matrix A n of order n is computed by means of their first two and last two columns or rows under the additional assumption that a certain 2 × 2 matrix is nonsingular. Moreover, a formula for the inverse of the Toeplitz-plus-Hankel matrix A n − 2 of order n − 2 in the center of A n is established and sufficient invertibility criteria for both A n and A n − 2 are obtained. Hereby a main tool is to use known inversion formulas involving not only rows or columns of the inverse but also solutions of equations the right hand sides of which depend on entries of the Toeplitz-plus-Hankel matrix itself. [ABSTRACT FROM AUTHOR]