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Table 2 Timings and errors for FMM runs for different N

From: A fast multipole method for stellar dynamics

N t tree t ffmm t up t walk t down { δ a / f } rms { δ a / f } 99.99 %
104 0.0004 0.0011 0.0012 0.0317 0.0005 2.81 × 10−7 1.32 × 10−6
105 0.0019 0.0042 0.0097 0.2131 0.0044 3.61 × 10−7 2.51 × 10−6
106 0.0290 0.0245 0.0957 1.5366 0.0431 3.85 × 10−7 3.32 × 10−6
107 0.2559 0.1897 0.8870 11.358 0.3999 4.05 × 10−7 2.20 × 10−6
  1. The runs used p = 10 and ϵ = 10−6.25. The timings are given in seconds and refer to, respectively, the tree building; the estimation of f via low-order FMM; the passing up of z, s, min{f}, and M n m ; the dual tree walk; and the passing down of F n m and evaluation of gravity. See also Figure 11.