Related papers: Thinplate Splines on the Sphere
This paper begins by reviewing numerous theoretical advancements in the field of multivariate splines, primarily contributed by Professor Larry L. Schumaker. These foundational results have paved the way for a wide range of applications and…
An oscillatory pattern in the smoothed quantum spectrum, which is unique for single-particle motions in a reflection-asymmetric superdeformed oscillator potential, is investigated by means of the semiclassical theory of shell structure.…
We present a multipolar model of surface - lattice resonances (SLRs) in 2d arrays of spheres including the electric dipole, magnetic dipole, and electric quadrupole moments of the spheres. We identify SLRs of dipolar and multipolar…
In this note we discuss solutions of differential equation $(D^2-\alpha^2)^{k}u=0$ on $\mathbb{R}\setminus\mathbb{Z}$, which we call hyperbolic splines. We develop the fundamental function of interpolation and prove various properties…
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given.…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that…
Three forms of representation of trigonometric interpolation splines are considered, in particular, the representation by the coefficients of the interpolation trigonometric polynomial, the representation by trigonometric B-splines, which…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…
Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the…
Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules.…
We investigate the emergence of finite-amplitude non-zonal flows on the sphere $\mathbb{S}^2$ arising from stationary solutions to the 2D Euler equations. By restricting the Laplace-Beltrami eigenspace to the invariant subspace of the…
We introduce the notion of multiplication kernels of birational and $D$-module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its…
Every simple quadrangulation of the sphere is generated by a graph called a pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of simple quadrangulations of the sphere." Discrete Math., Vol. 305, No. 1-3, pp. 33-54,…
This work presents a new interpolation tool, namely, cubic $q$-spline. Our new analogue generalizes a well known classical cubic spline. This analogue, based on the Jackson $q$-derivative, replaces an interpolating piecewise cubic…
In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…