Cholesky Factors Generating Positive Definite Symmetric Hankel Matrices

HANKEL_PDS is a C++ library which can compute a lower triangular matrix L which is the Cholesky factor of a positive definite (symmetric) Hankel matrix H, that is, H = L * L'.

A Hankel matrix is a matrix which is constant along all antidiagonals. A schematic of a 5x5 Hankel matrix would be:

        a  b  c  d  e
        b  c  d  e  f
        c  d  e  f  g
        d  e  f  g  h
        e  f  g  h  i

Let J represent the exchange matrix, formed by reverse the order of the columns of the identity matrix. If H is a Hankel matrix, then J*H and J*H are Toeplitz matrices, and similarly in the other direction. Hence many algorithms that apply to one class can be easily adapted to the other.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


HANKEL_PDS is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ASA006, a C++ library which computes the Cholesky factorization of a symmetric positive definite matrix, by Michael Healy. This is a MATLAB version of Applied Statistics Algorithm 6;

HANKEL_CHOLESKY, a C++ library which computes the upper Cholesky factor R of a nonnegative definite symmetric Hankel matrix H so that H = R' * R..


  1. S Al-Homidan, M Alshahrani,
    Positive Definite Hankel Matrices Using Cholesky Factorization,
    Computational Methods in Applied Mathematics,
    Volume 9, Number 3, 2009, pages 221-225.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 27 January 2017.