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Description


20.
If FACT = 'E', then real scaling factors $S_i$ are computed to equilibrate the system:

\begin{displaymath}[diag(S) A\: diag(S)][diag(S)^{-1} X] = diag(S) B\end{displaymath}

Depending on the value of EQUED determined during the equilibration, the matrix $diag(S)$ may be implicitly the identity matrix:

\begin{displaymath}\begin{array}{c\vert c}
{\bf EQUED} & diag({\bf S}) \\ \hlin...
...ty \\ \hline
\mbox{'Y'} & diag({\bf S}) \\ \hline
\end{array}\end{displaymath}

21.
If FACT = 'N', the Cholesky decomposition is used to factor the matrix $A$ as

\begin{displaymath}A = U^H U \mbox{ if {\bf UPLO} = 'U', or }
A = L\:L^H \mbox{ if {\bf UPLO} = 'L'},\end{displaymath}

where $U$ is an upper triangular matrix and $L$ is a lower triangular matrix ($L=U^H$). If FACT = 'E', the equilibrated matrix is factored as $U^HU$ or $LL^H$.
22.
If the leading minor of order $i$ of (the equilibrated) $A$ is not positive definite, then the routine returns with ${\bf INFO} = i$. Otherwise, an estimate of the condition number of (the equilibrated) $A$ is found using the above factorization. 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.
23.
LA_PBSVX also optionally computes, for each solution vector $X_j$, the estimated forward error bound and the componentwise relative backward error.



next up previous contents index
Next: Arguments Up: Symmetric/Hermitian Positive Definite Linear Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19