
\subsection{\bf Scalar Products in Parallel Conjugate Gradient}

\begin{slide}

\begin{itemize}
\item When one calculates $\sum_j A_{ij} x_j$, send $x_j$ to all
processors ``owning'' $x_i$ where $A_{ij} \neq 0$

\item This gives local communication

\item When one calculates \[ \sum_{j=1}^n y_j x_j \]
First calculate sums in a given processor, summing in Processor $P$
over all nodal points $j$ in $P$.  Then one must form

\hspace{1em} $\bullet$ a Global ``combine''.
\[ \sum_{\mbox{Processors}\ P} \left\lbrack \sum_{j\epsilon P} 
y_j x_j \right\rbrack \]

Typically, this same sum must be sent to all processors.
\end{itemize}

\end{slide}

