
\subsection{\bf Comparison of Convergence of}
\subsection{\bf Gauss-Seidel and Jacobi Iteration}

\begin{slide}

\begin{itemize}
\item Convergence can be characterized by a given fractional error (say .001).

\item This correponds to

\begin{displaymath}
\vert\lambda\vert^k_{\max} \sim .001
\end{displaymath}
where $k$ number of required iterations

\item $\exp \left\lbrack -k \left( 1- \left\vert \lambda
\right\vert_{\rm max}\right) \right\rbrack = .001$

i.e., value of $k \propto \frac{1}{\left(1-\vert\lambda\vert_{\rm
max}\right)}$

\item We showed Gauss Seidel doubles value of 
\begin{displaymath}
1/(1- \vert \lambda\vert_{\rm max}),
\end{displaymath}
i.e., it converges in half as many iterations as Jacobi
\end{itemize}

\end{slide}

