Related papers: On Polyharmonic Interpolation
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator $(-\Delta)^m$ with $ m \geq 2$. We show that the map from the coefficients to a certain bilinear form is injective. We…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…
Solutions to Laplace's equation are called harmonic functions. Harmonic functions arise in many applications, such as physics and the theory of stochastic processes. Of interest classically are harmonic polynomials, which have a simple…
We present a novel barycentric interpolation algorithm designed for analytic functions $f\in\mathcal{A}(E)$ defined on the complex plane. The algorithm, which encompasses both polynomial and rational interpolation, is tailored to handle…
In this paper we extend the Shepard-Bernoulli operators introduced in [6] to the bivariate case. These new interpolation operators are realized by using local support basis functions introduced in [23] instead of classical Shepard basis…
The purpose of this article is to provide new error estimates for a popular type of SBF approximation on the sphere: approximating by linear combinations of Green's functions of polyharmonic differential operators. We show that the $L_p$…
In the present paper we introduce a new concept of Hardy type space naturally defined on the Klein-Dirac quadric. We study different properties of the functions belonging to these spaces, in particular boundary value problems. We apply…
On a finite graph with a chosen partition of the vertex set into interior and boundary vertices, a $\lambda$-polyharmonic function is a complex function $f$ on the vertex set which satisfies $(\lambda \cdot I - P)^n f(x) = 0$ at each…
Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index of the main products of graphs. Here, we obtain several…
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…
We outline the super-resolution reconstruction problem posed as a maximization of probability. We then introduce an interpolation method based on polygonal pixel overlap, express it as a linear operator, and use it to improve…
In the monograph Kounchev, O. I., Multivariate Polysplines. Applications to Numerical and Wavelet Analysis, Academic Press, San Diego-London, 2001, and in the paper Kounchev O., Render, H., Cardinal interpolation with polysplines on annuli,…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
For $\alpha>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal B^p_\alpha$ of harmonic functions on the real hyperbolic ball and obtain an atomic decomposition of these spaces in terms of reproducing kernels. We show that an…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…