hankel_cholesky

hankel_cholesky, a Python code which computes the upper Cholesky factor of a symmetric positive definite (SPD) 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 symmetric 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 MIT 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:

hankel_spd, a Python code 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'.

toeplitz_cholesky, a Python code which computes the Cholesky factorization of a symmetric positive definite (SPD) 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.py, the source code.
• hankel_cholesky.sh, runs all the tests.
• hankel_cholesky.txt, the output file.