Re: Determinant of a matrix

[Gert Van den Eynde <gvdeynde@sckcen.be>]

Could you send us some lines of code that gives this behaviour and some more machine/compiler specs (see the Bug reporting part in the README file).

Remark 1: If I understand correctly, you calculate a determinant of 0.5E+13 and the error between Cholesky and LU is 6.0E+1 (a relative error of about 1.0E-11). 

Remark 2: The condition number of a Hilbert matrix of size 10 x 10 is about 1.0E+10. Roughly said, if you solve a linear system using LU factorisation (Gauss) with this matrix, you can loose about 10 decimal digits in your result... With the traditional double precision (u = 2.2E-16), this leaves you with 4 digits you can trust.... Hilbert matrices are *not* nice. 

Gert


On Tue, 22 Oct 2002 12:01:02 +0200
Przemyslaw Sliwa <sliwa@euv-frankfurt-o.de> wrote:

> 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
>