Analytic properties of moments matrices

Associated with each matrix element of the Generalized Moments Expansion, GMX(n,m) there is a unique expansion for the ground state energy in terms of the “connected moments” Ik of the Hamiltonian. That is, for any set {n,m} a polynomial in the Ik's may be generated to any desired order L, which is dependent upon the highest moment calculated. Here we wish to study the eigenvectors and eigenvalues of the GMX matrix itself. Furthermore we investigate the interplay between the set {n,m} and the order L of the matrix in determining which combination {n,m,L} yields the “best” (i.e. most convergent) result for the ground state energy.