This survey discusses recent developments in the context of spherical designs and minimal
energy point configurations on spheres. The recent solution of the long standing problem of …

This paper develops a fully discrete soft thresholding polynomial approximation over a
general region, named Lasso hyperinterpolation. This approximation is an \ell_1-regularized …

This paper considers a fully discrete filtered polynomial approximation on the unit sphere S^
d. For f ∈ C (S^ d), V_ L, N^(a)\, f is a polynomial approximation which is exact for all …

This paper investigates the role of quadrature exactness in the approximation scheme of
hyperinterpolation. Constructing a hyperinterpolant of degree n requires a positive-weight …

Spherical needlets are highly localized radial polynomials on the sphere S d⊂ R d+ 1, d≥
2, with centers at the nodes of a suitable cubature rule. The original semidiscrete spherical …

Spherical radial-basis-based kernel interpolation abounds in image sciences, including
geophysical image reconstruction, climate trends description, and image rendering, due to …

Abstract The Cubed Sphere grid is an important tool to approximate functions or data on the
sphere. We introduce an approximation framework on this grid based on least squares and …

We develop exterior calculus approaches for partial differential equations on radial
manifolds. We introduce numerical methods that approximate with spectral accuracy the …

This paper considers filtered polynomial approximations on the unit sphere S^ d ⊂ R^ d+ 1
S d⊂ R d+ 1, obtained by truncating smoothly the Fourier series of an integrable function f …

In this paper we consider the approximation of noisy scattered data on the sphere by radial
basis functions generated by a strictly positive definite kernel. The approximation is the …