This book is written as an introduction to analysis on the sphere and on the ball, and it
provides a cohesive account of recent developments in approximation theory and harmonic …

Meshfree approximation methods are a relatively new area of research, and there are only a
few books covering it at present. Whereas other works focus almost entirely on theoretical …

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 …

Recent theoretical work has shown that massively overparameterized neural networks are
equivalent to kernel regressors that use Neural Tangent Kernels (NTKs). Experiments show …

Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …

Radial Basis Function (RBF) methods have become the primary tool for interpolating
multidimensional scattered data. RBF methods also have become important tools for solving …

Error estimates for scattered-data interpolation via radial basis functions (RBFs) for target
functions in the associated reproducing kernel Hilbert space (RKHS) have been known for a …

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 …

This paper proposes and studies a numerical method for approximation of posterior
expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size …

This work investigates the prediction performance of the kriging predictors. We derive some
error bounds for the prediction error in terms of non-asymptotic probability under the uniform …