Numerical differentiation on scattered data through multivariate polynomial interpolation

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...

On multivariate polynomial interpolation

We provide a map Θ 7→ ΠΘ which associates each finite set Θ of points in C with a polynomial space ΠΘ from which interpolation to arbitrary data given at the points in Θ is possible and uniquely so. Among all polynomial spaces Q from which interpolation at Θ is uniquely possible, our ΠΘ is of smallest degree. It is also Dand scale-invariant. Our map is monotone, thus providing a Newton form for...

Lectures on Multivariate Polynomial Interpolation

Multivariate Polynomial Interpolation and the Lifting Scheme with an Application to Scattered Data Approximation

This thesis deals with generalized inverses, multivariate polynomial interpolation and approximation of scattered data. Moreover, it covers the lifting scheme, which basically links the aforementioned topics. For instance, determining filters for the lifting scheme is connected to multivariate polynomial interpolation. More precisely, sets of interpolation sites are required that can be interpo...

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...