HANKEL_PDS
Cholesky Factors Generating Positive Definite Symmetric Hankel Matrices

HANKEL_PDS is a Python 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.

Licensing:

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

Languages:

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:

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

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:

• hankel_pds.py
• hankel_pds.sh
• hankel_pds.txt, the output file.

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