Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space structure can be instrumental in improving accuracy and enhancing robustness with respect to noise. We demonstrate a three-pronged procedure for robust called PES: (1) Projection data space. (2) Estimation pole locations. (3) Semidefinite relaxation within compare performance PES recently developed Nevanlinna Carath\'{e}odory methods find that more presence noise does not require usage extended precision arithmetics. also projection improves methods. The method generalized bosonic response functions, which have yet been developed. It particularly useful studying spectra sharp features, as they occur study molecules band structures solids.