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## [Help-gsl] Linear algebra precision guarantee for LU_det

**From**: |
Jernej Azarija |

**Subject**: |
[Help-gsl] Linear algebra precision guarantee for LU_det |

**Date**: |
Thu, 8 Oct 2015 15:29:47 +0200 |

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

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