Related papers: Multivariate approximation by translates of the Ko…
This note is devoted to discussing multivariate approximation of continuous functions on $[0,1]^d$ with analytic Korobov kernels in the worst and average case settings. We only consider algorithms that use finitely many evaluations of…
Smolyak's method, also known as hyperbolic cross approximation or sparse grid method, is a powerful tool to tackle multivariate tensor product problems solely with the help of efficient algorithms for the corresponding univariate problem.…
This manuscript develops a framework for the strong approximation of Sobolev maps with values in compact manifolds, emphasizing the interplay between local and global topological properties. Building on topological concepts adapted to VMO…
We study methods based on reproducing kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process (MRP). We study a regularized form of the kernel least-squares temporal difference (LSTD)…
This paper describes an extension of Fourier approximation methods for multivariate functions defined on the torus $\mathbb{T}^d$ to functions in a weighted Hilbert space $L_{2}(\mathbb{R}^d, \omega)$ via a multivariate change of variables…
It is known that for a $\rho$-weighted $L_q$-approximation of single variable functions $f$ with the $r$th derivatives in a $\psi$-weighted $L_p$ space, the minimal error of approximations that use $n$ samples of $f$ is proportional to…
Approximation by polynomials on a triangle is studied in the Sobolev space $W_2^r$ that consists of functions whose derivatives of up to $r$-th order have bounded $L^2$ norm. The first part aims at understanding the orthogonal structure in…
We consider linear approximation based on function evaluations in reproducing kernel Hilbert spaces of certain analytic weighted power series kernels and stationary kernels on the interval $[-1,1]$. Both classes contain the popular Gaussian…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…
Let $\phi$ be a quasiconformal mapping, and let $T_\phi$ be the composition operator which maps $f$ to $f\circ\phi$. Since $\phi$ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins…
We constructed linear algorithms of sampling recovery and cubature formulas on Smolyak grids parametrized by $m \in \mathbb{N}$ of periodic $d$-variate functions having Lipschitz-H\"older mixed smoothness $\alpha > 0$ based on B-spline…
We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…
In this paper we obtained some direct and inverse theorems of approximation theory for $\psi$-differentiable functions in the metric weighted Orlicz spaces with weights, which belong to the class of Muckenhoupt.
We revisit the Karagiannidis-Lioumpas (KL) approximation of the Q-function by optimizing its coefficients in terms of absolute error, relative error and total error. For minimizing the maximum absolute/relative error, we describe the…
The concept of mixed norm spaces has emerged as a significant interest in fields such as harmonic analysis. In addition, the problem of function approximation through sampling series has been particularly noteworthy in the realm of…
For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an…
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…
The famous results of Koml\'os, Major and Tusn\'ady (see [15] and [17]) state that it is possible to approximate almost surely the partial sums of size n of i.i.d. centered random variables in L p (p > 2) by a Wiener process with an error…
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the "native" Hilbert space $\calh$ in which they are reproducing. Continuous kernels on compact domains have an expansion into…
Spectral approximation by polynomials on the unit ball is studied in the frame of the Sobolev spaces $W^{s}_p(\ball)$, $1<p<\infty$. The main results give sharp estimates on the order of approximation by polynomials in the Sobolev spaces…