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If ${\bf FACT}$ = 'N', the $LU$ decomposition is used to factor the matrix $A$ as $A = LU$, where $L$ is a product of permutation and unit lower bidiagonal matrices and $U$ is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.
If some $U_{i,i}=0$, so that $U$ is singular, then the routine returns with ${\bf INFO} = i$. Otherwise, the factored form of $A$ is used to estimate the condition number of $A$. If the reciprocal of the condition number is less than machine precision, ${\bf INFO} = n+1$, where $n$ is the order of $A$, is returned as a warning. However, the routine still goes on to solve for $X$. Iterative refinement is applied to improve the computed solution.
LA_GTSVX also optionally computes, for each solution vector $X_j$ the estimated forward error bound and the componentwise backward error.

Susan Blackford 2001-08-19