Related papers: Hermite-type interpolation in terms of exponential…
This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space $\mathbb R^3$ (where they are equivalent to the PN surfaces) and in the…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
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…
Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
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…
We consider the question when the so--called spectral condition} for Hermite subdivision schemes extends to spaces generated by polynomials and exponential functions. The main tool are convolution operators that annihilate the space in…
In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for…
We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
We consider $\mathbb{L}_2$-approximation of elements of a Hermite space of analytic functions over $\mathbb{R}^s$. The Hermite space is a weighted reproducing kernel Hilbert space of real valued functions for which the Hermite coefficients…
In this paper we study the singularity of multivariate Hermite interpolation of type total degree. We present a method to judge the singularity of the interpolation scheme considered and by the method to be developed, we show that all…
The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered. The proposed method is based on the periodicity properties…
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…
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and…
In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.
Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even…
In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…