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## Copyright (C) 1996 John W. Eaton
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, write to the Free
## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
## usage: invhilb (n)
##
## Return the inverse of a Hilbert matrix of order n. This is slow but
## exact. Compare with inv (hilb (n)).
##
## See also: hankel, vander, sylvester_matrix, hilb, toeplitz
## Author: jwe
function retval = invhilb (n)
if (nargin != 1)
usage ("invhilb (n)");
endif
nmax = length (n);
if (nmax == 1)
retval = zeros (n);
for l = 1:n
for k = l:n
tmp = 1;
for i = 1:n
tmp = tmp * (i + k - 1);
endfor
for i = 1:n
if (i != k)
tmp = tmp * (l + i - 1);
endif
endfor
for i = 1:n
if (i != l)
tmp = tmp / (i - l);
endif
endfor
for i = 1:n
if (i != k)
tmp = tmp / (i - k);
endif
endfor
retval (k, l) = tmp;
retval (l, k) = tmp;
endfor
endfor
else
error ("hilb: expecting scalar argument, found something else");
endif
endfunction
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