Many practical applications require the reconstruction of a multivariate function from
discrete, unstructured data. This book gives a self-contained, complete introduction into this …

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 …

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

The moving least squares (MLS) method provides an approximation û of a function u based
solely on values u (xj) of u on scattered 'meshless' nodes x j. Derivatives of u are usually …

Optimal transport (OT) is a versatile framework for comparing probability measures, with
many applications to statistics, machine learning and applied mathematics. However, OT …

We study the use of Gaussian process emulators to approximate the parameter-to-
observation map or the negative log-likelihood in Bayesian inverse problems. We prove …

This work is concerned with the convergence of Gaussian process regression. A particular
focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in …

It is well-known that plug-in statistical estimation of optimal transport suffers from the curse of
dimensionality. Despite recent efforts to improve the rate of estimation with the smoothness …

The first chapters of this book deal with Haar bases, Faber bases and some spline bases for
function spaces in Euclidean $ n $-space and $ n $-cubes. These are used in the …

This book combines two mathematical branches: dynamical systems and radial basis
functions. It is mainly written for mathematicians with experience in at least one of these two …