Determinant of a matrix

[Przemyslaw Sliwa <sliwa@euv-frankfurt-o.de>]

Hello,

The determinant of a symmetric positive definite matrix is just the
product of the squares of the diagonal elements form the cholesky
decomposition (NAG documentation). So why I'm getting different
results form gsl_LU decomposition and the cholesky decomposition
of a 10*10 Hilbert matrix (elemenst i,j given by 1/(i+j-1)).
The results are not very big, but still they exist (determinant about 
0.5E+13 and
the difference 6.0E+1). Is it a bug, or the LU decomposition is unstable.
What should be suggested: determinant of a covariance matrix: its
Cholesky form or computation from LU decomposition.

Thanks for help

Przem