APPROXIMATION BY A HERMITIAN POSITIVE SEMIDEFINITE TOEPLITZ MATRIX

The problem of finding the nearest Hermitian positive semidefinite Toe plitz matrix (in the Frobenius norm) of a given rank to an arbitrary m atrix is considered. A special orthogonal basis and equally spaced fre quencies allow good initial approximations. A second method using alte rnating projections solves the case of unrestricted rank. Some interes ting numerical results suggest possible applications to signal process ing problems.