hankel_cholesky

hankel_cholesky, an Octave code which computes the upper Cholesky factor R 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 an Octave version and a Python version.

Related Data and Programs:

hankel_cholesky_test

asa006, an Octave code which computes the Cholesky factorization R of a symmetric positive definite (SPD) matrix, by Michael Healy. This is a MATLAB version of Applied Statistics Algorithm 6;

hankel_inverse, an Octave code which computes the inverse of a Hankel matrix.

hankel_spd, an Octave 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, an Octave 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_upper.m, computes the upper Cholesky factor of a Hankel matrix.
• hankel_spd_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 symmetric positive definite (SPD) 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.