Reliable Pade analytical continuation method based on a high-accuracy symbolic computation algorithm

We critique a Pade analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure, is accomplished to an extremely high accuracy using a symbolic computation algorithm. As an-example of this method in action, it is applied to the problem of determining the spectral function of a single-particle thermal Green's function known only at a finite number of Matsubara frequencies with two example self energies drawn from the T-matrix theory of the Hubbard model. We present a systematic analysis of the effects,of error in the input points on the analytic continuation, and this leads us to propose a procedure to test:quantitatively the reliability of the resulting continuation, thus eliminating the black-magic label frequently attached to this procedure.