The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …

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

In this paper we wish to present a new class of tight frames on the sphere. These frames
have excellent pointwise localization and approximation properties. These properties are …

In this paper we present error estimates for kernel interpolation at scattered sites on
manifolds. The kernels we consider will be obtained by the restriction of positive definite …

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 …

A new numerical technique based on radial basis functions (RBFs) is presented for fitting a
vector field tangent to the sphere, S^2, from samples of the field at “scattered” locations on …

In this paper, we aim at developing scalable neural network-type learning systems.
Motivated by the idea of constructive neural networks in approximation theory, we focus on …

The purpose of this paper is to establish $ L^ p $ error estimates, a Bernstein inequality, and
inverse theorems for approximation by a space comprising spherical basis functions located …

Quadrature formulas for spheres, the rotation group, and other compact, homogeneous
manifolds are important in a number of applications and have been the subject of recent …