Speed and Adaptability of Overlap Fermion Algorithms

TL;DR

This paper compares four algorithms for computing the overlap Dirac operator, focusing on their speed and adaptability, and finds that the Zolotarev rational approximation is the fastest and most adaptable method.

Contribution

It provides a comparative analysis of algorithms for overlap fermion computations, highlighting the efficiency and adaptability of the Zolotarev approximation.

Findings

Zolotarev approximation is the fastest and most adaptable.

Orthogonal polynomial expansions are fast but non-adaptable.

Conjugate gradient approximation is nearly as fast and self-tuning.

Abstract

We compare the efficiency of four different algorithms to compute the overlap Dirac operator, both for the speed, i.e., time required to reach a desired numerical accuracy, and for the adaptability, i.e., the scaling of speed with the condition number of the (square of the) Wilson Dirac operator. Although orthogonal polynomial expansions give good speeds at moderate condition number, they are highly non-adaptable. One of the rational function expansions, the Zolotarev approximation, is the fastest and is adaptable. The conjugate gradient approximation is adaptable, self-tuning, and nearly as fast as the ZA.