%Eigenvalue Power Method
%If you modify this file, please indicate here and in the footnote
%Math410

\documentclass[12pt]{article}
\usepackage{times}
\pagestyle{empty}

\addtolength{\textwidth}{1.2in}
\addtolength{\textheight}{1.2in}
\addtolength{\oddsidemargin}{-.58in}
\addtolength{\evensidemargin}{-.58in}
\renewcommand{\baselinestretch}{1.0}
\parindent = 0cm
\parskip = .1cm

\begin{document}

\begin{center}
{\Large
Eigenvalue Power Method\footnote{
Copyright \copyright 2002 Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}}
\end{center}

\begin{enumerate}
 \item Enter the following sequence of commands:\\
	\verb&   format long&\\
        \verb&   A = hilb(5);&\\
        \verb&   m = eig(A)&\\
        \verb&   v = ones(5,1)&\\
        \verb&   w = v./norm(v);&

\item Next enter the following sequence:\\
        \verb&   v = A*w;&\\
        \verb&   w = v./norm(v);&\\
        \verb&   ma = w'*A*w&

\item Repeat the steps in part 2 until the value of
        \verb&ma& stops changing.  How many iteratations did it take?
        Is this number close to one of the eigenvalues?
        How close?

\item Repeat the above experiment for the Pascal matrix generated by: 
	\verb& A = pascal(5)&.

\item Repeat the experiment for a larger matrix.


\item Using complete sentences and standard mathematical notation, write a brief report.
\end{enumerate}

\vfill

\noindent
\textsf{This demonstrates the simplest form of the QR method. Most modern software
including \textsc{Matlab's} built-in function ``eig" use improved versions of this algorithm. }

\end{document}

