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Description


30.
If FACT = 'N', a diagonal pivoting method is used to factor the matrix $A$ as

\begin{displaymath}A = U\, D\, U^T \mbox{ if {\bf UPLO} = 'U', or }
A = L\, D\,...
...box{ if {\bf UPLO} = 'L'}\hspace{1.50 cm}(\mbox{\bf LA\_SPSVX})\end{displaymath}

or

\begin{displaymath}A = U\, D\, U^H \mbox{ if {\bf UPLO} = 'U', or }
A = L\, D\,...
...box{ if {\bf UPLO} = 'L'}\hspace{1.50 cm}(\mbox{\bf LA\_HPSVX})\end{displaymath}

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric (LA_SPSVX) or Hermitian (LA_HPSVX) and block diagonal with $1 \times 1$ and $2 \times 2$ diagonal blocks.
31.
If some $D_{i,i}=0$, so that $D$ is singular, then the routine returns with ${\bf INFO} = i$. Otherwise, the factored form of $A$ is used to estimate the condition number of the matrix $A$. 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.
32.
LA_SPSVX and LA_HPSVX also optionally compute, 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 Indefinite Linear Systems Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19