Gohberg-Semencul type formula and application for the inverse of a conjugate-Toeplitz matrix involving imaginary circulant matrices

Abstract

Gohberg-Semencul type inverse formula of conjugate-Toeplitz (CT) is obtained by constructing a kind of imaginary cyclic displacement transform. The stability of decomposition formula of inverse is investigated, and its algorithm is also given. Numerical example is provided to verify the feasibility of the inverse formula. How the analogue of our formula leads to a more efficient way to solve the conjugate-Toeplitz linear system of equations is proposed. The corresponding inverse, stability, and algorithm of conjugate-Hankel (CH) matrix are also considered.