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pro vyhledávání: '"Kunsch, Robert"'
Autor:
Kunsch, Robert J., Wnuk, Marcin
We study approximation of the embedding $\ell_p^m \hookrightarrow \ell_q^m$, $1 \leq p < q \leq \infty$, based on randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance where $n \ll m$. By analysing
Externí odkaz:
http://arxiv.org/abs/2410.23067
Autor:
Kunsch, Robert J., Wnuk, Marcin
We study approximation of the embedding $\ell_p^m \rightarrow \ell_{\infty}^m$, $1 \leq p \leq 2$, based on randomized adaptive algorithms that use arbitrary linear functionals as information on a problem instance. We show upper bounds for which the
Externí odkaz:
http://arxiv.org/abs/2408.01098
Autor:
Kunsch, Robert J.
We study the numerical integration of functions from isotropic Sobolev spaces $W_p^s([0,1]^d)$ using finitely many function evaluations within randomized algorithms, aiming for the smallest possible probabilistic error guarantee $\varepsilon > 0$ at
Externí odkaz:
http://arxiv.org/abs/2309.09059
We prove lower bounds for the randomized approximation of the embedding $\ell_1^m \rightarrow \ell_\infty^m$ based on algorithms that use arbitrary linear (hence non-adaptive) information provided by a (randomized) measurement matrix $N \in \mathbb{R
Externí odkaz:
http://arxiv.org/abs/2308.01705
Publikováno v:
In Journal of Approximation Theory December 2024 304
The dispersion of a point set in $[0,1]^d$ is the volume of the largest axis parallel box inside the unit cube that does not intersect with the point set. We study the expected dispersion with respect to a random set of $n$ points determined by an i.
Externí odkaz:
http://arxiv.org/abs/1911.12074
Autor:
Kunsch, Robert J., Rudolf, Daniel
We study the complexity of approximating integrals of smooth functions at absolute precision $\varepsilon > 0$ with confidence level $1 - \delta \in (0,1)$. The optimal error rate for multivariate functions from classical isotropic Sobolev spaces $W_
Externí odkaz:
http://arxiv.org/abs/1809.09890
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a sample size ba
Externí odkaz:
http://arxiv.org/abs/1805.08637
Autor:
Kunsch, Robert J.
We study the $L_1$-approximation of $d$-variate monotone functions based on information from $n$ function evaluations. It is known that this problem suffers from the curse of dimensionality in the deterministic setting, that is, the number $n(\vareps
Externí odkaz:
http://arxiv.org/abs/1803.00099