Reduced ringing-artifacts in our enhanced hybrid algorithm. Left panel: the convolution of point sources with a Gaussian kernel of 4.7′ FWHM using a FSHT-based algorithm at nside = 2048 causes extended residuals. Right panel: the result obtained with ARKCoS only shows a suppressed ringing pattern in the longitudinal direction in the polar caps (upper four point sources). In the equatorial region, the artifacts cancel out exactly (lower four point sources). Each patch is 13° on the side, the logarithmic color scale counts representing factors of 10 from the maximum. For ARKCoS, the ringing patterns are too small to be visible on a linear scale.
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