MinimaL eigenvalue of a real symmetric positive definite Toeplitz matrix

摘要

The problem of computing the minimal eigenvalue of a real symmetric positive definite Toeplitz matrix is considered. Algorithms for estimating such an eigenvalue, which need only one or two inverses, are presented. The suggested algorithms are based on good initial approximations to the corresponding eigenvector which can be derived by approximating the Toeplitz matrix by circulant matrices.