
\subsection{\bf Clarification of Eigenvalue Analysis}
\subsection{\bf for Conjugate Gradient}
\subsection{\bf and Jacobi Iteration}

\begin{slide}

\begin{itemize}
\item Note in eigenvalues:\ In Jacobi/SOR, ``large'' eigenvalues
converged slowly, ``small'' eigenvalues converged fast.

\item But the matrices aren't the same.

\item Conjugate gradient (CG) uses complete matrix {\bf A}

\item SOR uses decomposed matrix $\bf A=M+N$

\item $M^{-1}N$ eigenvalues determine SOR

$\bf A$ eigenvalues determine CG

\item Large eigenvalues of {\bf A} $\rightarrow$ small eigenvalues of
SOR and vice versa.
\end{itemize}

\end{slide}

