
\subsection{\bf Estimate of Marquardt}

\subsection{\bf Parameter Q}

\begin{slide}
\begin{itemize}
\item One needs an artistic method to estimate $Q$ which again is
varied based on experience.  $Q$ is increased when predicted 
\[
\chi^2
\left( \Underline{$\beta$}_0 + \Delta\beta \right) > \chi^2 \left(
\Underline{$\beta$}_0 \right)
\]
and is otherwise decreased or left unchanged.

\item The natural ``scale'' for $Q$ is given by
\[
\frac{1}{n}\, T\, r\, {\bf M} = \frac{1}{n}\, \sum^n_{j=1} \lambda_j
\]
the average eigenvalue.

\item Marquardt's method is less precise than the diagonalization
method but much faster; 

\item finding eigenvalues and vectors is time consuming.
\end{itemize}
\end{slide}

