Padé analytical continuation method based on a high accuracy symbolic computation algorithm

We critique a Padé 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 novel 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 Tmatrix 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. Typeset using REVTEX 1