

\subsection{\bf The Real World and $\chi^2$}
\subsection{\bf Minimization---II}

\begin{slide}
\begin{itemize}
\item $\chi^2$ will have a bunch of hills and valleys and we are
trying to discover the location of the lowest point in the valley.  

\item If our assumptions are correct, then $\chi^2$ is just a neat
quadratic function, and we have found a step that exactly moves to the
minimum.

\vspace*{15pt}
\centerline{\psfig{figure=fig15.phys.ps,clip=true,width=4.5in}}
\vspace*{10pt}

\item Unfortunately, this is not usually correct, as the step
$\Underline{$\alpha$}_0 \rightarrow \Underline{$\alpha$}_0 +
\Delta\Underline{$\alpha$}$ {\em maybe too large\/} to support the
assumption, that terms in $\frac{\partial^k (\chi^2)}{\partial\alpha^k}$,
$k\ge 3$ are zero, to be correct.
\end{itemize}
\end{slide}

