A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
Abstract
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 novel symbolic computation algorithm. As an example of this method in action we apply it to the problem of determining the spectral function of a one-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.
Keywords
Cite
@article{arxiv.cond-mat/9908477,
title = {A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm},
author = {K. S. D. Beach and R. J. Gooding and F. Marsiglio},
journal= {arXiv preprint arXiv:cond-mat/9908477},
year = {2009}
}
Comments
11 pages, 8 eps figs, revtex format; revised version includes reference to anonymous ftp site containing example codes (MapleVr5.1 worksheets) displaying the implementation of the algorithm, including the padematinv.m library package