V. K. Nguyen

activity

20142026

most citedChange of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube

33 citations · 48 across the 19 of their papers we have counts for

collaborators

27 papers

math.FA2026

Triebel - Lizorkin spaces of dominating mixed smoothness are algebras with respect to pointwise multiplication

Van Kien Nguyen

We continue our investigations on pointwise multipliers for spaces of dominating mixed smoothness. In this paper we prove that under a certain conditions Triebel - Lizorkin spaces…

math.FA2026

Widths of embeddings of Gaussian Sobolev spaces

Van Kien Nguyen

In this paper, we investigate the approximation problem for functions in Gaussian Sobolev spaces $W_{p}^{s} (R^{d}, γ)$ of smoothness $s > 0$ , where the approximation error is me…

math.NA2026

Optimal numerical integration for functions in fractional Gaussian Sobolev spaces

Van Kien Nguyen

This paper investigates the numerical approximation of integrals for functions in fractional Gaussian Sobolev spaces $W_{p}^{s} (R^{d}, γ)$ with dominating mixed smoothness defi…

math.NA2026

Approximation of PDE solution manifolds: Sparse-grid interpolation and quadrature

Dinh Dũng, Van Kien Nguyen, Duong Thanh Pham +1

We study fully-discrete approximations and quadratures of infinite-variate functions in abstract Bochner spaces associated with a Hilbert space $X$ and an infinite-tensor-product J…

math.FA2023

Pseudo $s$ -Numbers of Embeddings of Gaussian Weighted Sobolev Spaces

Van Kien Nguyen

In this paper, we study the approximation problem for functions in the Gaussian-weighted Sobolev space $W_{p}^{α} (R^{d}, γ)$ of mixed smoothness $α \in N$ with error mea…

math.NA2022

Optimal numerical integration and approximation of functions on $R^{d}$ equipped with Gaussian measure

Dinh Dũng, Van Kien Nguyen

We investigate the numerical approximation of integrals over $R^{d}$ equipped with the standard Gaussian measure $γ$ for integrands belonging to the Gaussian-weighted Sobole…

math.NA2022

Analyticity of Parametric Elliptic Eigenvalue Problems and Applications to Quasi-Monte Carlo Methods

Van Kien Nguyen

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 r…

math.NA2022★ 3 cited

Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs

Dinh Dũng, Van Kien Nguyen, Christoph Schwab +1

We establish sparsity and summability results for coefficient sequences of Wiener-Hermite polynomial chaos expansions of countably-parametric solutions of linear elliptic and parab…

math.NA2021★ 1 cited

Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs

Dinh Dũng, Van Kien Nguyen, Duong Thanh Pham

We investigate non-adaptive methods of deep ReLU neural network approximation in Bochner spaces $L_{2} (U^{\infty}, X, μ)$ of functions on $U^{\infty}$ taking values i…

math.FA2021

Best $n$ -term approximation of diagonal operators and application to function spaces with mixed smoothness

Van Kien Nguyen, Van Dung Nguyen

In this paper we give exact values of the best $n$ -term approximation widths of diagonal operators between $ℓ_{p} (N)$ and $ℓ_{q} (N)$ with $0 < p, q \leq \infty$ . Th…

math.NA2021★ 1 cited

High-dimensional nonlinear approximation by parametric manifolds in Hölder-Nikol'skii spaces of mixed smoothness

Dinh Dũng, Van Kien Nguyen

We study high-dimensional nonlinear approximation of functions in Hölder-Nikol'skii spaces $H_{\infty}^{α} (I^{d})$ on the unit cube $I^{d} := [0, 1]^{d}$ having mixed smoothne…

math.FA2020

$s$ -Numbers of Embeddings of Weighted Wiener Algebras

Van Dung Nguyen, Van Kien Nguyen, Winfried Sickel

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}…

math.NA2020

Deep ReLU neural networks in high-dimensional approximation

Dinh Dũng, Van Kien Nguyen

We study the computation complexity of deep ReLU (Rectified Linear Unit) neural networks for the approximation of functions from the Hölder-Zygmund space of mixed smoothness define…

math.NA2019

Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances

Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen +1

The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational meth…

math.FA2018

Greedy Algorithms and Kolmogorov Widths in Banach Spaces

Van Kien Nguyen

Let $X$ be a Banach space and $K$ be a compact subset in $X$ . We consider a greedy algorithm for finding an $n$ -dimensional subspace $V_{n} \subset X$ which can be used to a…

math.NA2017★ 5 cited

Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness

Glenn Byrenheid, Robert J. Kunsch, Van Kien Nguyen

We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the toru…

math.FA2017

Pointwise Multipliers for Besov Spaces of Dominating Mixed Smoothness - II

Van Kien Nguyen, Winfried Sickel

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(\mathbb{…

math.FA2017★ 2 cited

On a Problem of Jaak Peetre Concerning Pointwise Multipliers of Besov Spaces

Van Kien Nguyen, Winfried Sickel

We characterize the set of all pointwise multipliers of the Besov spaces $B_{p, q}^{s} (R)$ under the restrictions $0 < p, q \leq \infty$ and $s > d / p$ .

math.FA2016

Isotropic and Dominating Mixed Lizorkin - Triebel Spaces - a Comparison

Van Kien Nguyen, Winfried Sickel

We shall compare isotropic Lizorkin-Triebel spaces with their counterparts of dominating mixed smoothness.

math.FA2016

Pointwise Multipliers for Sobolev and Besov Spaces of Dominating Mixed Smoothness

Van Kien Nguyen, Winfried Sickel

Under certain restrictions we describe the set of all pointwise multipliers in case of Sobolev and Besov spaces of dominating mixed smoothness. In addition we shall give necessary…

math.FA2016

Gelfand Numbers of Embeddings of Mixed Besov Spaces

Van Kien Nguyen

Gelfand numbers represent a measure for the information complexity which is given by the number of information needed to approximate functions in a subset of a normed space with an…

math.FA2016

Isotropic and Dominating Mixed Besov Spaces - a Comparison

Van Kien Nguyen, Winfried Sickel

We compare Besov spaces with isotropic smoothness with Besov spaces of dominating mixed smoothness. Necessary and sufficient conditions for continuous embeddings will be given.

math.NA2015★ 33 cited

Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube

Van Kien Nguyen, Mario Ullrich, Tino Ullrich

In a recent article by two of the present authors it turned out that Frolov's cubature formulae are optimal and universal for various settings (Besov-Triebel-Lizorkin spaces) of fu…

math.FA2015

Weyl and Bernstein Numbers of Embeddings of Sobolev Spaces with Dominating Mixed Smoothness

Van Kien Nguyen

This paper is a continuation of the papers [21] and [22]. Here we shall investigate the asymptotic behaviour of Weyl and Bernstein numbers of embeddings of Sobolev spaces with domi…

Triebel - Lizorkin spaces of dominating mixed smoothness are algebras with respect to pointwise multiplication

Widths of embeddings of Gaussian Sobolev spaces

Optimal numerical integration for functions in fractional Gaussian Sobolev spaces

Approximation of PDE solution manifolds: Sparse-grid interpolation and quadrature

Pseudo s-Numbers of Embeddings of Gaussian Weighted Sobolev Spaces

Optimal numerical integration and approximation of functions on Rd equipped with Gaussian measure

Analyticity of Parametric Elliptic Eigenvalue Problems and Applications to Quasi-Monte Carlo Methods

Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs

Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs

Best n-term approximation of diagonal operators and application to function spaces with mixed smoothness

High-dimensional nonlinear approximation by parametric manifolds in Hölder-Nikol'skii spaces of mixed smoothness

s-Numbers of Embeddings of Weighted Wiener Algebras

Deep ReLU neural networks in high-dimensional approximation

Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances

Greedy Algorithms and Kolmogorov Widths in Banach Spaces

Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness

Pointwise Multipliers for Besov Spaces of Dominating Mixed Smoothness - II

On a Problem of Jaak Peetre Concerning Pointwise Multipliers of Besov Spaces

Isotropic and Dominating Mixed Lizorkin - Triebel Spaces - a Comparison

Pointwise Multipliers for Sobolev and Besov Spaces of Dominating Mixed Smoothness

Gelfand Numbers of Embeddings of Mixed Besov Spaces

Isotropic and Dominating Mixed Besov Spaces - a Comparison

Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube

Weyl and Bernstein Numbers of Embeddings of Sobolev Spaces with Dominating Mixed Smoothness

Pseudo $s$ -Numbers of Embeddings of Gaussian Weighted Sobolev Spaces

Optimal numerical integration and approximation of functions on $R^{d}$ equipped with Gaussian measure

Best $n$ -term approximation of diagonal operators and application to function spaces with mixed smoothness

$s$ -Numbers of Embeddings of Weighted Wiener Algebras