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pro vyhledávání: '"Wasilkowski, G. W."'
In the present paper we study quasi-Monte Carlo rules for approximating integrals over the $d$-dimensional unit cube for functions from weighted Sobolev spaces of regularity one. While the properties of these rules are well understood for anchored So
Externí odkaz:
http://arxiv.org/abs/2001.05765
On alternative quantization for doubly weighted approximation and integration over unbounded domains
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 $\|\omega^{1/\
Externí odkaz:
http://arxiv.org/abs/1907.04015
In this paper, we study the approximation of $d$-dimensional $\rho$-weighted integrals over unbounded domains $\mathbb{R}_+^d$ or $\mathbb{R}^d$ using a special change of variables, so that quasi-Monte Carlo (QMC) or sparse grid rules can be applied
Externí odkaz:
http://arxiv.org/abs/1812.04259
Publikováno v:
Journal of Complexity 54 (2019), article 101406
We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh, Haar, and S
Externí odkaz:
http://arxiv.org/abs/1809.07103
The paper considers truncation errors for functions of the form $f(x_1,x_2,\dots)=g(\sum_{j=1}^\infty x_j\,\xi_j)$, i.e., errors of approximating $f$ by $f_k(x_1,\dots,x_k)=g(\sum_{j=1}^k x_j\,\xi_j)$, where the numbers $\xi_j$ converge to zero suffi
Externí odkaz:
http://arxiv.org/abs/1709.02113
The paper considers linear problems on weighted spaces of multivariate functions of many variables. The main questions addressed are: When is it possible to approximate the solution for the original function of very many variables by the solution for
Externí odkaz:
http://arxiv.org/abs/1701.06778
We consider approximation of functions of $s$ variables, where $s$ is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very small number $
Externí odkaz:
http://arxiv.org/abs/1610.02852
We provide lower bounds for the norms of embeddings between $\boldsymbol{\gamma}$-weighted Anchored and ANOVA spaces of $s$-variate functions with mixed partial derivatives of order one bounded in $L_p$ norm ($p\in[1,\infty]$). In particular we show
Externí odkaz:
http://arxiv.org/abs/1511.05674
We consider the problem of numerical integration for weighted anchored and ANOVA Sobolev spaces of $s$-variate functions. Here $s$ is large including $s=\infty$. Under the assumption of sufficiently fast decaying weights, we prove in a constructive w
Externí odkaz:
http://arxiv.org/abs/1506.02458
Autor:
Wasilkowski, G. W., Wozniakowski, H.
Publikováno v:
Mathematics of Computation, 2001 Apr 01. 70(234), 685-698.
Externí odkaz:
https://www.jstor.org/stable/2698775
