

\subsection{\bf Marquardt's Method}

\begin{slide}
\begin{itemize}
\item Marquardt's method is a simpler technique but with similar goals
to the eigenvalue method.  

\item One replaces
\[
{\bf M} \rightarrow {\bf M} + QI
\]

\item where {\bf I} is the identity matrix.  

\item So this means we replace $M$ by

\vspace*{10pt}
\centerline{\psfig{figure=fig20.phys.ps,clip=true,width=4.0in}}
\vspace*{10pt}

\item Clearly, if $\lambda_L \sim Q$, then the two formalism's are
roughly equivalent.

\item Eigenvectors with eigenvalues $>Q$, are shifted by naive
prediction while those with eigenvalue $<<Q$, have their shift
drastically reduced.
\end{itemize}
\end{slide}

