function lambda = powermethod(A, xinitial, niters)
% POWERMETHOD : Power method to estimate norm of dominant eigenvalue
%
% lambda = powermethod(A, xinitial, niters);
%
% This routine takes matrix A and vector xinitial, and repeatedly
% multiplies the matrix by the vector and normalizes the result
% to have length 1.
% If the dominant eigenvalue of A is simple, the vector converges 
% to the dominant eigenvector and the norm converges to the norm 
% of the dominant eigenvalue, which is returned.
%
% This routine does exactly niters iterations.
% (A more realistic power method routine would include a test
%  to see when the iteration converged.)
%
% This is a sequential Matlab template -- CS240A homework 1 is
% to implement this in parallel.
%
% John R. Gilbert    13 Jan 2006

n = length(xinitial);
x = xinitial;
for i = 1:niters
    x = x / norm(x);
    x = A * x;
end;
lambda = norm(x);