%Eigenvalue Power Method
%If you modify this file, please indicate here and in the footnote
%Math410
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{\Large
Eigenvalue Power Method\footnote{
Copyright \copyright 2002 Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}}
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\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}
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\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. }
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