Power method to determine largest real eigenvalue does not converge

I have written a function as per the pseudocode to determine the maximum eigenvalue of a given nxn matrix given a specified tolerance value. Unfortunately my anwser does not converge. The vector seems to be unchanged after the first 50-60 iterations so i attempted to caclulate the eigenvalue at the 55th iteration by calculating the infinite norm of the corresponding vector. The anwser is not close at all. Any assistance would be appreciated (i have attached the pseudocode as a PNG).

% M = randi(15,5)/10;
% A = M'*M;
A = [1 2 1; 6 -1 0; -1 -2 -1];
[V,D] = eig(A)
[e,v]= power_method(A,1e-4)


function [eigen_value,vector]= power_method(A,tol)
% Write you code here
x0 = randi([1,5],length(A),1); %arbitrary vector x0
vector = x0; %start with arbitrary vector x0
iter = 1; %iteration counter
while 1
    vector_old = vector;
    vector = A*vector;
    eigen_value = norm(vector,inf);
    vector = vector/max(vector);
    error = norm(vector - vector_old);
    if error<tol
        break
    end    
    iter = iter + 1;
end

iter
error
end

[Umar Mirza]

Did some more investigation and figured out that my A matrix is singular. Method seems to work fine for a non-singular matrix. I'm assuming that the power method only works for non-singular matrices, ie. invertible?

Answer 1

[Bruno Luong]

The png is not correct if A has negative largest eigan (absolute) value

Try this

A = [1 2 1; 6 -1 0; -1 -2 -1];
[V,D] = eig(A)
[e,v]= power_method(A,1e-4)


function [eigen_value,vector]= power_method(A,tol)
% Write you code here
x0 = randi([1,5],length(A),1); %arbitrary vector x0
vector = x0; %start with arbitrary vector x0
iter = 1; %iteration counter
while 1
    vector_old = vector;
    vector = A*vector;
    [~,imax] = max(abs(vector));
    maxv = vector(imax);
    vector = vector/maxv;
    error = norm(vector - vector_old);
    if error<tol
        break
    end    
    iter = iter + 1;
end
eigen_value = maxv
iter
end

[Umar Mirza]

Thanks. Is the comment i made to my original post above valid?

[Bruno Luong]

No