Supplement to “Strictly and non-strictly positive definite functions on spheres”. Appendix A
states and proves further criteria of Pólya type, thereby complementing Section 4.2 …

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 chapter is concerned with numerical integration over the unit sphere $${\mathbb
{S}}^{2}\subset {\mathbb {R}}^{3} $$. We first discuss basic facts about numerical integration …

Large-scale computer experiments are becoming increasingly important in science. A multi-
step procedure is introduced to statisticians for modeling such experiments, which builds an …

We proposed ways to implement meshless collocation methods extrinsically for solving
elliptic PDEs on smooth, closed, connected, and complete Riemannian manifolds with …

We present three new semi-Lagrangian methods based on radial basis function (RBF)
interpolation for numerically simulating transport on a sphere. The methods are mesh-free …

In recent years mathematicians and researchers within the approximation theory community
have become increasingly interested in using tools from approximation theory to develop …

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

In industry and economics, the most common solutions of partial differential equations
involving multivariate numerical integration over cuboids include techniques of iterated one …

This paper focuses on the approximation of continuous functions on the unit sphere by
spherical polynomials of degree n via hyperinterpolation. Hyperinterpolation of degree n is a …