  In this paper, we compare two optimization algorithms using full Hessian and
approximation Hessian to obtain numerical spherical designs through their
variational characterization. Based on the obtained spherical design point
sets, we investigate the approximation of smooth and non-smooth functions by
spherical harmonics with spherical designs. Finally, we use spherical framelets
for denoising Wendland functions as an application, which shows the great
potential of spherical designs in spherical data processing.
