This article presents a new algorithm for obtaining a block diagonalization of Hankel matrices by means of truncated polynomial divisions, such that every block is a lower Hankel matrix. In fact, the algorithm generates a block LU-factorization of the matrix. Two applications of this algorithm are also presented. By the one hand, this algorithm yields an algebraic proof of Frobenius' Theorem, which gives the signature of a real regular Hankel matrix by using the signs of its principal leading minors. On the other hand, the close relationship between Hankel matrices and linearly recurrent sequences leads to a comparison with the Berlekamp-Massey algorithm. © 2005 Elsevier Inc. All rights reserved.
Ben Atti, N., & Diaz-Toca, G. M. (2006). Block diagonalization and LU-equivalence of Hankel matrices. Linear Algebra and Its Applications, 412(2–3), 247–269. https://doi.org/10.1016/j.laa.2005.06.029