Recurrence relations for the even and odd characteristic polynomials of a symmetric Toeplitz matrix

• DOI: 10.1016/j.cam.2004.03.022
• Publication Date: 2004-06-02T20:58:06Z
• Authors: Aleksandra Kostić; Heinrich Voss
• Keywords: Recurrence relation; Matrix (chemical analysis); Levinson recursion

In a recent paper [10] Melman proved an even–odd factorization of the characteristic polynomial of a symmetric Toeplitz matrix T on which a symmetry exploiting method for computing the smallest eigenvalue of T can be based. In this note we present a proof of the factorization which is less technical and more transparent.