Computation of the Smallest Even and Odd Eigenvalues of a Symmetric Positive-Definite Toeplitz Matrix

Abstract

We propose an algorithm to compute the smallest even and odd eigenvalues of a real symmetric positive-definite Toeplitz matrix, which is based on the factorization of the characteristic polynomial into an even and an odd polynomial. Newton's method is used to compute the smallest even and odd eigenvalues as the smallest roots of the even and odd characteristic polynomials, respectively.