  We propose an algebraic method for extracting excited states from lattice
gauge theory correlation functions. Instead of fitting to a sum of decaying
exponentials, we adopt a variant of Prony's method to obtain $M$ energies
(exponential decay rates) by finding the roots of an $M^{\rm th}$ order
polynomial, and then solving for the amplitudes linearly. The resulting states
tend to have overlapping error ellipses, making identification of states
ambiguous. This is especially problematic at large Euclidean times where the
signal to noise may be low, as well as when many states are extracted. We
propose a variation of K-means clustering to identify each extracted state.
