 For instance, by keeping not just the last vector in the sequence, but instead looking at the span of "all" the vectors in the sequence, one can get a better (faster converging) approximation for the eigenvector, and this idea is the basis of Arnoldi iteration.Alternatively, the important QR algorithm is also based on a subtle transformation of a power method.Once the eigenvalues are computed, the eigenvectors could be calculated by solving the equation

using Gaussian elimination or any other method for solving matrix equations.