HANKEL_CHOLESKY
Cholesky Factor of a Positive Definite Hankel Matrix

HANKEL_CHOLESKY is a MATLAB library which can compute the upper Cholesky factor of a positive definite (symmetric) Hankel matrix H, that is, H = R' * R.

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
      

Licensing:

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

Languages:

HANKEL_CHOLESKY 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_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'.

TOEPLITZ_CHOLESKY, a MATLAB library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.

Reference:

1. James Phillips,
   The triangular decomposition of Hankel matrices,
   Mathematics of Computation,
   Volume 25, Number 115, July 1971, pages 599-602.

Source Code:

• hankel_cholesky_upper.m, computes the upper Cholesky factor of a Hankel matrix.
• 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_cholesky_factor_upper.m, computes the upper Cholesky factor of an R8MAT.
• 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.

Examples and Tests:

• hankel_cholesky_test.m, calls all the tests;
• hankel_cholesky_upper_test.m.
• hankel_cholesky_test.txt, the output file.

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