Power Method Eigenvectors Code

I am attempting to make a code for a manual computation of the Power Method.

I think I have it working properly but wanted to make sure. Any thoughts?

function [lambda,x,k] = power_method(A,x,tol,maxit); 
% Initialize
n = length(A);
k = 0;
y = zeros(1,n);
tolerance = 1;

while k < maxit && (tolerance > tol)
        yk = A * x; % y(k) = A* x(k)
        xnext = yk / norm(yk); % X(k+1) = yk / 2norm(yk)
        lambda = dot (xnext,(A * xnext)); % lambda = X(k+1) * (A * X(k+1))
        k = k + 1;
        tolerance = norm(yk - lambda * x);
        err = tolerance;
        x = xnext;
end

[James Tursa]

What do you mean by "look smoother"?

[Benjamin Boettcher]

It seems to work, I guess I just wanted it verified. and see if it could be made any better.

Answer 1

[James Tursa]

The only obvious thing I would note is that the following line doesn't accomplish anything because you don't use err in your code, so it can be removed:

err = tolerance;

[Benjamin Boettcher]

Thanks. That was an artifact from the generation of this.