Newton type methods for computing the smallest eigenvalue of a symmetric Toeplitz matrix

Abstract

Several methods for computing the smallest eigenvalue of asymmetric positive definite Toeplitz matrix are presented. They converge from the left to the minimum eigenvalue, and they rely on Newton's method and interpolation of the characteristic polynomial with no need for introductory bisection steps. The methods are conceptually much simpler than the ones introduced by the same authors based on rational interpolation of the secular equation.