相关论文: Sparse grid approximation in weighted Wiener space…
We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of…
In this paper, we analyze the convergence behavior of Hermite-type sampling Kantorovich operators in the context of mixed norm spaces. We prove certain direct approximation theorems, including the uniform convergence theorem, the…
The parameters of a neural network are naturally organized in groups, some of which might not contribute to its overall performance. To prune out unimportant groups of parameters, we can include some non-differentiable penalty to the…
We introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), mapping a compact interval $[a,b]$ into the space of compact non-empty subsets of ${\mathbb R}^d$. All operators are adapted by…
Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation between the spatial variable and the parameter. In this…
The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…
This paper investigates a time discrete variational model for splines in Wasserstein spaces to interpolate probability measures. Cubic splines in Euclidean space are known to minimize the integrated squared acceleration subject to a set of…
This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial…
The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be used for approximating high-dimensional functions and, in particular, for surrogate-model-based uncertainty quantification. It is lightweight,…
In recent years, it has been well understood that a Calder\'on-Zygmund operator $T$ is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar pointwise…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
The purpose of this article is to give a Chlodowsky type generalization of Szasz operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order…
In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on…
In the present paper, we introduce a Choldowsky type generalization of the q Favard-Szasz operators and obtain weighted statistical approximation properties of these operators. We also establish the rates of statistical convergence by means…
This paper continues the study of interpolation operators on scattered data. We introduce the Poisson interpolation operator and prove various properties. The main result concerns functions in the Paley-Wiener space $PW_{B_\beta}$, and…
In this paper multivariate extension of the generalized Durrmeyer sampling type series are considered. We establish a Voronovskaja type formula and a quantitative version. Finally some particular examples are discussed.
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…