[qwerty1793]

The largest eigenvalue of (A - k)^{-1} is 1 / (x - k) where x is the smallest eigenvalue of A that is larger than k. So by using this technique on (A - k)^{-1} for various values of k you can find all of the eigenvalues of A.

[acidburnNSA]

In practice this is numerically unstable and it's generally better to use methods that use a larger and orthogonal subspace (i.e. Krylov methods) to get multiple eigenvalue/vectors. In nuclear reactor problems you can maybe get about 5 eigenvalues by filtering the larger ones but after that it gets noisy fast. I've gotten up to 1000 good eigenvalues from a large neutron diffusion problem using Arnoldi.