hankel_spd


hankel_spd, a C++ library which can compute a lower triangular matrix L which is the Cholesky factor of a symmetric positive definite (SPD) 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.

Licensing:

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

Languages:

hankel_spd 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 (SPD) 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 symmetric positive definite (SPD) Hankel matrix H so that H = R' * R..

hankel_spd_test

Reference:

  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:


Last revised on 11 March 2020.