MINIMAL EIGENVALUE OF A REAL SYMMETRICAL POSITIVE-DEFINITE TOEPLITZ MATRIX

The problem of computing the minimal eigenvalue of a real symmetric po sitive definite Toeplitz matrix is considered. Algorithms for estimati ng such an eigenvalue, which need only one or two inverses, are presen ted. The suggested algorithms are based on good initial approximations to the corresponding eigenvector which can be derived by approximatin g the Toeplitz matrix by circulant matrices.