  Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's
(or related) method (PM), are commonly used to analyze statistical estimates of
correlation functions produced in lattice quantum field theory calculations.
GEM takes full advantage of the matrix structure of correlation functions but
only considers individual pairs of time separations when much more data exists.
PM can be applied to many time separations and many individual matrix elements
simultaneously but does not fully exploit the matrix structure of the
correlation function. We combine both these methods into a single framework
based on matrix polynomials. As these algebraic methods are well known for
producing extensive spectral information about statistically-noisy data, the
method should be paired with some information criteria, like the recently
proposed Bayesean model averaging.
