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
