Zobrazeno 1 - 10
of 159
pro vyhledávání: '"Nguyen, Van Kien"'
Autor:
Nguyen, Van Kien
In this paper, we study the approximation problem for functions in the Gaussian-weighted Sobolev space $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $\alpha \in \mathbb{N}$ with error measured in the Gaussian-weighted space $L_q(\mathbb{R}^d
Externí odkaz:
http://arxiv.org/abs/2309.11309
Autor:
Dũng, Dinh, Nguyen, Van Kien
We investigate the numerical approximation of integrals over $\mathbb{R}^d$ equipped with the standard Gaussian measure $\gamma$ for integrands belonging to the Gaussian-weighted Sobolev spaces $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $
Externí odkaz:
http://arxiv.org/abs/2207.01155
Analyticity of Parametric Elliptic Eigenvalue Problems and Applications to Quasi-Monte Carlo Methods
Autor:
Nguyen, Van Kien
In the present paper, we study the analyticity of the leftmost eigenvalue of the linear elliptic partial differential operator with random coefficient and analyze the convergence rate of the quasi-Monte Carlo method for approximation of the expectati
Externí odkaz:
http://arxiv.org/abs/2202.02530
We establish sparsity and summability results for coefficient sequences of Wiener-Hermite polynomial chaos expansions of countably-parametric solutions of linear elliptic and parabolic divergence-form partial differential equations with Gaussian rand
Externí odkaz:
http://arxiv.org/abs/2201.01912
We investigate non-adaptive methods of deep ReLU neural network approximation in Bochner spaces $L_2({\mathbb U}^\infty, X, \mu)$ of functions on ${\mathbb U}^\infty$ taking values in a separable Hilbert space $X$, where ${\mathbb U}^\infty$ is eithe
Externí odkaz:
http://arxiv.org/abs/2111.05854
Autor:
Nguyen, Van Kien, Nguyen, Van Dung
In this paper we give exact values of the best $n$-term approximation widths of diagonal operators between $\ell_p(\mathbb{N})$ and $\ell_q(\mathbb{N})$ with $0
Externí odkaz:
http://arxiv.org/abs/2108.12974
The purpose of the present paper is to study the computation complexity of deep ReLU neural networks to approximate functions in H\"older-Nikol'skii spaces of mixed smoothness $H_\infty^\alpha(\mathbb{I}^d)$ on the unit cube $\mathbb{I}^d:=[0,1]^d$.
Externí odkaz:
http://arxiv.org/abs/2103.00815
Autor:
Dũng, Dinh, Nguyen, Van Kien
We study high-dimensional nonlinear approximation of functions in H\"older-Nikol'skii spaces $H^\alpha_\infty(\mathbb{I}^d)$ on the unit cube $\mathbb{I}^d:=[0,1]^d$ having mixed smoothness, by parametric manifolds. The approximation error is measure
Externí odkaz:
http://arxiv.org/abs/2102.04370
In this paper we study the asymptotic behavior of Kolmogorov, approximation, Bernstein and Weyl numbers of embeddings $ \mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d) \to L_2(\mathbb{T}^d)$ and $\mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d) \to \mathcal{A}(\m
Externí odkaz:
http://arxiv.org/abs/2011.07663
Autor:
Dũng, Dinh, Nguyen, Van Kien
We study the computation complexity of deep ReLU (Rectified Linear Unit) neural networks for the approximation of functions from the H\"older-Zygmund space of mixed smoothness defined on the $d$-dimensional unit cube when the dimension $d$ may be ver
Externí odkaz:
http://arxiv.org/abs/2007.08729