Related papers: Spherical quasi-interpolation using scaled zonal k…
We establish a deterministic and stochastic spherical quasi-interpolation framework featuring scaled zonal kernels derived from radial basis functions on the ambient Euclidean space. The method incorporates both quasi-Monte Carlo and Monte…
We develop and analyze a class of matrix-valued spherical-convolution kernels stemming from scaled zonal functions on $\mathbb{S}^2,$ the unit sphere embedded in $\mathbb{R}^3$. The construct of these kernels utilizes the Legendre…
This paper focuses on developing a framework for constructing quasi-interpolation with the highest achievable approximation order from generalized Gaussian kernels with the help of kernel restriction trick and periodization technique. We…
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…
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…
In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…
Subdivision surfaces are considered as an extension of splines to accommodate models with complex topologies, making them useful for addressing PDEs on models with complex topologies in isogeometric analysis. This has generated a lot of…
The paper aims at proposing an efficient and stable quasi-interpolation based method for numerically computing the Helmholtz-Hodge decomposition of a vector field. To this end, we first explicitly construct a matrix kernel in a general form…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
In this paper, we present new quasi-interpolating spline schemes defined on 3D bounded domains, based on trivariate $C^2$ quartic box splines on type-6 tetrahedral partitions and with approximation order four. Such methods can be used for…
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 discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
We design a quasi-interpolation operator from the Sobolev space $H^1_0(\Omega)$ to its finite-dimensional finite element subspace formed by piecewise polynomials on a simplicial mesh with a computable approximation constant. The operator 1)…
Motivated by the recent multilevel sparse kernel-based interpolation (MuSIK) algorithm proposed in [Georgoulis, Levesley and Subhan, SIAM J. Sci. Comput., 35(2), pp. A815-A831, 2013], we introduce the new quasi-multilevel sparse…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange…
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we…