Table 1
Estimation of Fourier-Bessel coefficients: comparison of the new method, the reverse formulation (Eqs. (19) and (20) using HEALPix discretisation) with the original, raw formulation (Eq. (7)).
| N | nside | ϵr(fℓmn) < 0.3% | ϵr(Cℓn) < 0.3% | T | |
| [0, 20]/[21, 50] | [0, 20]/[21, 50] | ||||
|
|
|||||
| 4.2e5 | 512 | 87%/42% | 99%/96% | 8 | |
| 1024 | 95%/65% | 99%/98% | 4 | ||
| 2048 | 99%/84% | 99%/99% | 2 | ||
| 3.1e6 | 512 | 92%/50% | 99%/95% | 10 | |
| 1024 | 98%/74% | 100%/100% | 5 | ||
| 2048 | 99%/90% | 100%/100% | 2 | ||
| 9.7e6 | 512 | 92%/50% | 100%/97% | 12 | |
| 1024 | 97%/74% | 100%/100% | 6 | ||
| 2048 | 99%/90% | 100%/100% | 3 | ||
|
|
|||||
Notes. The third (fourth) column gives the percentage f coefficients for which the relative accuracy ϵ(fℓmn) (ϵ(Cℓn)) is lower than 0.3% for given values of nside and N. T is the ratio of elapsed times of the two methods.
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