Speed and Adaptability of Overlap Fermion Algorithms

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.