HANKEL_PDS
Cholesky Factors Generating Positive Definite Symmetric Hankel Matrices

HANKEL_PDS, a MATLAB 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 H*J 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:

ASA006, a MATLAB 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 MATLAB library which computes the upper Cholesky factor R of a nonnegative definite symmetric Hankel matrix H so that H = R' * R..

hankel_pds_test

Reference:

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_cholesky_lower.m, given data for the main diagonal and first subdiagonal, returns a lower triangular matrix L which is the lower Cholesky factor of a positive definite symmetric Hankel matrix.
r8mat_print.m, prints an R8MAT.
r8mat_print_some.m, prints some of an R8MAT.
r8vec_uniform_01.m, returns an R8VEC of random numbers in [0,1].
timestamp.m, prints the current YMDHMS date as a time stamp.