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 …

Many studies, mostly empirical, have been devoted to finding an optimal shape parameter
for radial basis functions (RBF). When exploring the underlying factors that determine what …

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

Hardy's multiquadric and its related interpolators have been found to be highly efficient for
interpolating continuous, multivariate functions, as well as for the solution of partial …

Positive definite kernels play an increasingly prominent role in many applications such as
scattered data fitting, numerical solution of PDEs, computer experiments, machine learning …

We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to
interpolation, boundary-value, and initial-boundary-value problems with localized features …

It is shown that no stable procedure for approximating functions from equally spaced
samples can converge exponentially for analytic functions. To avoid instability, one must …

This article reviews and studies the properties of Bayesian quadrature weights, which
strongly affect stability and robustness of the quadrature rule. Specifically, we investigate …

Approximating a function from its values f (xi) at a set of evenly spaced points xi through
(N+1)-point polynomial interpolation often fails because of divergence near the endpoints …

We show how the collocation framework that is prevalent in the radial basis function
literature can be modified so that the methods can be interpreted in the framework of …