# Power method to calculate eigenvectors

I've implemented a program for computing eigenvectors of some random, symmetric, $N$x$N$ matrix using the power method. I have found difficulty in calculating all $N$ eigenvectors consistently, almost every time the algorithm fails to converge for all $N$. The Wikipedia page on the power method tells me this algorithm is not guaranteed to converge for all $N$ eigenvectors, can someone suggest a way for me to encourage convergence, at least in a majority of the cases? Is this possible? If not, can someone suggest a better algorithm for computing eigenvectors?

• you have $O(1)$ access to the elements of the matrix or just the ability to apply it to vectors via a function call