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 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.

@article{
  title = {Reliable Pad\'e analytical continuation method based on a high-accuracy symbolic computation algorithm},
  author = {Beach, K. S. D. and Gooding, R. J. and Marsiglio, F.},
  journal = {Physical Review B},
  volume = {61},
  issue = {8},
  pages = {5147--5157},
  numpages = {0},
  year = {2000},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.61.5147},
  url = {http://link.aps.org/doi/10.1103/PhysRevB.61.5147}
}