A fast method to block-diagonalize a Hankel matrix

In this paper, we consider an approximate block diagonalization algorithm of an nxn real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a new fast approach to compute the factorization in O(n(2)) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511-523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur complementation adapted to the nxn real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness of our approach.