An eigenvalue recursion for Hermitian Toeplitz matrices

A recursive algorithm is developed for finding the eigenvalues of a Hermitian Toeplitz matrix order n. The algorithm presented represents a generalization to the Hermitian case of one proposed by D.M. Wilkes and M.H. Hayes (1987) for the symmetric Toeplitz case. The method proposed uses Levinson´s algorithm, or the more computationally efficient Hermitian Levinson algorithm of S.D. Morgera and H. Krishna (1987), at step k to form the characteristic equation of the next-larger principal submatrix of order k+1. The eigenvalues are then determined from the characteristic equation. The important issue of eigenvalue accuracy, which also applies to the Wilkes-Hayes procedure, is addressed