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of 5 460
pro vyhledávání: '"41A25"'
We prove sharp upper and lower bounds for the approximation of Sobolev functions by sums of multivariate ridge functions, i.e., functions of the form $\mathbb{R}^d \ni x \mapsto \sum_{k=1}^n h_k(A_k x) \in \mathbb{R}$ with $h_k : \mathbb{R}^\ell \to
Externí odkaz:
http://arxiv.org/abs/2412.08453
Autor:
García, Jonathan, Petersen, Philipp
We prove that a classifier with a Barron-regular decision boundary can be approximated with a rate of high polynomial degree by ReLU neural networks with three hidden layers when a margin condition is assumed. In particular, for strong margin conditi
Externí odkaz:
http://arxiv.org/abs/2412.07312
A new Goodman-Sharma modification of the Baskakov operator is presented for approximation of bounded and continuous on $[0,\,\infty)$ functions. In our study on the approximation error of the proposed operator we prove direct and strong converse theo
Externí odkaz:
http://arxiv.org/abs/2412.04586
$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation. Also recent
Externí odkaz:
http://arxiv.org/abs/2412.02489
Autor:
Goda, Takashi, Krieg, David
We present a simple universal algorithm for high-dimensional integration which has the optimal error rate (independent of the dimension) in all weighted Korobov classes both in the randomized and the deterministic setting. Our theoretical findings ar
Externí odkaz:
http://arxiv.org/abs/2411.19164
Autor:
Rieger, Christian, Wendland, Holger
In this paper, we show that the approximation of high-dimensional functions, which are effectively low-dimensional, does not suffer from the curse of dimensionality. This is shown first in a general reproducing kernel Hilbert space set-up and then sp
Externí odkaz:
http://arxiv.org/abs/2411.18128
In many applications, random fields reflect uncertain parameters, and often their moments are part of the modeling process and thus well known. However, there are practical situations where this is simply not the case. Therefore, we do not assume tha
Externí odkaz:
http://arxiv.org/abs/2412.00027
Autor:
Sinha, Arghya, Chaudhury, Kunal N.
The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play ($\texttt{PnP}$) and Regularization-by-Denoising ($\texttt{RED}$). We consider two speci
Externí odkaz:
http://arxiv.org/abs/2411.10808
Let $f$ be a real function defined on the interval $[0,1]$ which is constant on $(a,b)\subset [0,1]$, and let $B_nf$ be its associated $n$th Bernstein polynomial. We prove that, for any $x\in (a,b)$, $|B_nf(x)-f(x)|$ converges to $0$ as $n\rightarrow
Externí odkaz:
http://arxiv.org/abs/2411.10135
Autor:
Kolomoitsev, Yurii, Tikhonov, Sergey
We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results show that the Bernstein inequality in a general quasi-Banach function
Externí odkaz:
http://arxiv.org/abs/2411.04119