Speed and Adaptability of Overlap Fermion Algorithms
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, has reasonable speed and may be useful if an adaptable version of the algorithm can be constructed. The conjugate gradient approximation turns out to be extremely adaptable and has acceptable speed even when the condition number becomes of the order of 10^5--10^9.Keywords
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