On a Newton Method for the Inverse Toeplitz Eigenvalue Problem

Iterative methods for inverse eigenvalue problems involve simultaneous approximation of the matrix being sought and its eigenvectors This paper revisits one such method for the inverse Toeplitz eigenvalue problems by exploring the eigenstructure of centrosymmetric matrices All itera tions are now taking place on a much smaller subspace One immediate consequence is that the size of the problem is e ectively cut in half and hence the cost of computation is substantially reduced Another advantage is that eigenvalues with multiplicity up to two are necessarily separated into to disjoint blocks and hence division by zero is unmistakably avoided Numerical experiment seems to indicate that the domain of convergence is also improved In addition a new scheme by using the Wielandt Ho man theorem is proposed This new mechanism makes it possible to handle the case when eigenvalues with multiplicity greater than two are present