[Help-gsl] Linear algebra precision guarantee for LU_det

[Jernej Azarija]

Hello!

I am working with n x n symmetric matrices where the diagonal elements
are 28/9 and off-diagonal elements are either -8/9 or 1/9.

For any such given matrix I need to determine  whether its determinant
is negative or not. I need to be sure not to mark a matrix with
non-negative determinant as having a negative determinant (I m fine if
the converse mistake is made).

Right now I am just using checking whether the computed determinant is
smaller than a generous threshold but I would like to have a provable
error estimate as to be 100% sure I do not skip a matrix with
non-negative determinant.

Now I've noticed that some of the linear algebra routines in GSL  come
with a precision bound, however I couldn't find anything for what is
used in this case, namely  gsl_linalg_LU_decomp and
gsl_linalg_LU_decomp_DET.

Hence I was wondering - is there any way to obtain a sensible bound to
determine whether the of such a matrix is in fact negative or not?

Best,

Jernej