Computation of symmetric positive definite Toeplitz matrices by the hybrid steepest descent method

This paper studies the problem of finding the nearest symmetric positive definite Toeplitz matrix to a given symmetric one. Additional design constraints, which are also formed as closed convex sets in the real Hilbert space of all symmetric matrices, are imposed on the desired matrix. An algorithmic solution to the problem given by the hybrid steepest descent method is established also in the case of inconsistent design constraints.