Description

24.

If FACT = 'N', the matrix $A$ is factored as $A = LDL^H$, where $L$ is a unit lower bidiagonal matrix and $D$ is a diagonal matrix. The factorization can also be regarded as having the form $A = U^H D U$, where $U = L^H$.

25.

If the leading minor of order $i$ of $A$ is not positive definite, 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.

26.

LA_PTSVX also optionally computes, for each solution vector $X_j$, the estimated forward error bound and the componentwise relative backward error.