Approximating potential integrals by cardinal basis interpolants on multivariate scattered data

Scattered data approximation of fully fuzzy data by quasi-interpolation

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...

Multivariate Refinable Hermite Interpolants

We introduce a general definition of refinable Hermite interpolants and investigate their general properties. We study also a notion of symmetry of these refinable interpolants. Results and ideas from the extensive theory of general refinement equations are applied to obtain results on refinable Hermite interpolants. The theory developed here is constructive and yields an easy-to-use constructi...

Reconstruction of Multivariate Functions from Scattered Data

Monotonicity Preserving Approximation of Multivariate Scattered Data ∗

This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming ...

Multivariate Rational Interpolation of Scattered Data

Abstract. Rational data fitting has proved extremely useful in a number of scientific applications. We refer among others to the computation of cell loss probabilities in network traffic [5, 6, 14, 15], to the modelling of electro-magnetic components [20, 12] to model reduction of linear shift-invariant systems [2, 3, 7] and so on. When computing a rational interpolant in one variable, all exis...