Related papers: Classical multivariate Hermite coordinate interpol…
We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the…
In this note we explicit the notion of Hermite interpolant of a multivariate symmetric polynomial, generalizing the notion of Lagrange interpolant to the case when there are roots coalescence, an extension of the results on the symmetric…
Spline quasi-interpolation (QI) is a general and powerful approach for the construction of low cost and accurate approximations of a given function. In order to provide an efficient adaptive approximation scheme in the bivariate setting, we…
Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…
The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
We characterize the sets of solvability for Hermite multivariate interpolation problems when the sum of multiplicities is at most $2n + 2$, with $n$ the degree of the polynomial space. This result extends an earlier theorem (2000) by one of…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. We prove a generalization of this to higher dimensional varieties, showing that smooth varieties of minimal degree can be interpolated…
We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow…
We compute minimal bases of solutions for a general interpolation problem, which encompasses Hermite-Pad\'e approximation and constrained multivariate interpolation, and has applications in coding theory and security. This problem asks to…
This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both…
This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general…