
\subsection{\bf Convergence of Conjugate Gradient}

\begin{slide}

\begin{itemize}
\item The number of conjugate gradient iterations needed for given
accuracy for simple problems (positive definite matrix {\bf A}) is
given by
\begin{eqnarray*}
k & = & \sqrt{\frac{\lambda_{\max}}{\lambda_{\min}}} \\
& \propto & \frac{1}{h}
\end{eqnarray*}
where $h$ is grid size

\item Remember SOR was $1/h$ $\underline{\rm if}$ overrelaxation
parameter $w$ chosen correctly, which is not easy.

\item Jacobi and Gauss Seidel have a number of iterations $k \propto
1/h^2$ which is much more

\item Conjugate gradient iterations are more complicated and time
consuming than those for Jacobi or Gauss Seidel
\end{itemize}

\end{slide}

