If a given matrix $A$ is known to have three different and real eigenvalues $\lambda_1$, $\lambda_2$ and $\lambda_3$ and we know that they are near $-2$, $2$ and $10$ respectively (using Gershgorin's circle theorem), how would we use the power method to find the value of all the eigenvalues without resorting to "shifting" the power method?
In the event that there are multiple ways of doing this, what would be the simplest way using the Power Method?