arXiv:hep-lat/0110198·v1·High Energy Physics — Lattice
A comparative study of numerical methods for the overlap Dirac operator--a status report
J. van den Eshof🇳🇱 · A. Frommer🇩🇪 · Th. Lippert🇩🇪 · K. Schilling🇩🇪 · H.A. van der Vorst🇳🇱
Abstract
Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks show that this PFE together with removal of converged systems within a multi-shift CG appears to approximate the sign function times a vector most efficiently. A posteriori error bounds are given.
Comments: 3 pages, poster contribution to Lattice2001(algorithms)