A symmetry exploiting Lanczos method for symmetric Toeplitz matrices

Several methods for computing the smallest eigenvalues of a symmetric and positive definite Toeplitz matrix T have been studied in the literature. Most of them share the disadvantage that they do not reflect symmetry properties of the corresponding eigenvector. In this note we present a Lanczos method which approximates simultaneously the odd and the even spectrum of T at the same cost as the classical Lanczos approach.