function [gamma, x] = poweriter(A, numiter)
% POWERITER   Power iteration for the dominant eigenvalue.
% Input:
%   A         square matrix
%   numiter   number of iterations
% Output: 
%   gamma     sequence of eigenvalue approximations (vector)
%   x         final eigenvector approximation
    n = length(A);
    x = randn(n, 1);
    x = x/norm(x, inf);
    gamma = zeros(numiter,1);
    for k = 1:numiter
        y = A*x;
        [~, m] = max(abs(y));
        gamma(k) = y(m)/x(m);
        x = y/y(m);
    end 
end