

\subsection{\bf The Real World and $\chi^2$ Minimization}
\subsection{\bf Example of Two Variables---I}

\begin{slide}
\begin{itemize}
\item Consider the case when there are two variables.
\begin{eqnarray*}
\chi^2 & = & \chi^2_0 + \mbox{linear terms} \\
& + & A_1 \left( \alpha_1 - \alpha_1^0 \right)^2 + A_2 \left( \alpha_2 - 
\alpha_2^0 \right)^2 \\
& + & B_1 \left( \alpha_1 - \alpha_1^0 \right)^3 + B_2 \left( \alpha_1 - 
\alpha_1^0 \right)^2 \left( \alpha_2 - \alpha_2^0 \right) + \ldots \\
& + & \ldots
\end{eqnarray*}

\item where we have taken the special case where there is no term
proportional to $(\alpha_1 - \alpha_1^0) (\alpha_2 - \alpha_2^0)$;

\item such a term only confuses the current discussion, and we will
soon see how to put it back in.

\item The difficulty (lack of convergence of iterative scheme) occurs
when
\[
A_1 >> A_2
\]
\end{itemize}
\end{slide}

