Re: Extracting the dominant eigenvector

[A. Scottedward Hodel]

You need to be cautious: is the 10x10 matrix symmetric/hermitian?  If not, 
you may have complex eigenvalues, and the sort procedure may give you 
unexpected results.  

In the symmetric case, take a look at Golub and Van Loan's book, Matrix 
Computations, in the chapter "The Symmetric Eigenvalue Problem."  (Or 
Beresford Parlett's book, 1984, by the same title.)

A power iteration may work if the largest eigenvalue is significantly larger 
than the other eigenvalues:

while( not converged)
  w = A*v
  v   = w/norm(w)
endwhile

If you've got a good estimate of the largest eigenvalue, you can use

while (not converged)
  w = (A - lambda*eye(*n))\v
  v = w/norm(w)
endwhile

to accelerate convergence.

Hope that helps some.

Quoting Mike Miller <address@hidden>:

> On Thu, 28 Mar 2002, Stefan Jonsson wrote:
> 
> > Hello octave users
> >
> > I have what I hope is a simple problem
> >
> > I have a square matrix, A, currently 10by10, may at
> > later time have different dimensions.
> >
> > asking for eigenvalues and eigen vectors
> >
> > [vect, val] =eig(A); 
> >
> > I need the dominant eigenvalue and corresponding eigenvector
> 
> 
> I suppose this will work for square matrix A of any size:
> 
> k=size(A,1);
> [V,D]=eig(A);
> [S,I]=sort(diag(D));
> val=S(k);
> vec=V(:,I(k));
> 
> You could write it as a function like this: [val, vec] = maxeig(A)
> 
> I use the 'sort' function which returns index I.  Read "help sort".
> 
> Regards,
> 
> Mike
> 
> -- 
> Michael B. Miller, Ph.D.
> Assistant Professor
> Division of Epidemiology
> University of Minnesota
> http://taxa.epi.umn.edu/~mbmiller/
> 
> 
> 
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A. S. Hodel Assoc Prof Dept. Elect. Eng., 200 Broun Hall

Auburn University, Auburn AL 36849-5201 
http://www.eng.auburn.edu/~scotte



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