Dũng Dinh

activity

20102026

most citedHyperbolic Cross Approximation

26 citations · 46 across the 28 of their papers we have counts for

collaborators

31 papers

math.NA2026

Local Gevrey regularity and Quasi-Monte Carlo quadrature for PDEs parameterized on non-compact domains

Dinh Dũng, Tùng Lê, Alexey Chernov

We establish local Gevrey regularity for the weak solution to parametric divergence-form diffusion elliptic PDEs, assuming the diffusion coefficient itself possesses local Gevrey p…

math.NA2025

Laguerre- and Laplace-weighted integration of mixed-smoothness functions

Dinh Dũng

We investigate the approximation of generalized Laguerre- or Laplace-weighted integrals over $R_{+}^{d}$ or $R^{d}$ of functions from generalized Laguerre- or Laplace-w…

math.NA2025

Simultaneous spatial-parametric collocation approximation for parametric PDEs with log-normal random inputs

Dinh Dũng

We establish convergence rates for a fully discrete, multi-level, linear collocation method solving parametric elliptic PDEs on bounded polygonal domains with log-normal inputs. Th…

math.NA2024

Sampling recovery in Bochner spaces and applications to parametric PDEs

Felix Bartel, Dinh Dũng

We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coeff…

math.NA2024

Weighted hyperbolic cross polynomial approximation

Dinh Dũng

We study linear polynomial approximation of functions in weighted Sobolev spaces $W_{p, w}^{r} (R^{d})$ of mixed smoothness $r \in N$ , and their optimality in terms of…

math.NA2024

Weighted sampling recovery of functions with mixed smoothness

Dinh Dũng

We studied linear weighted sampling algorithms and their optimality for approximate recovery of functions with mixed smoothness on $R^{d}$ from a set of $n$ their sampled va…

math.NA2023

Sparse-grid sampling recovery and numerical integration of functions having mixed smoothness

Dinh Dũng

We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smo…

math.NA2022

Numerical weighted integration of functions having mixed smoothness

Dinh Dũng

We investigate the approximation of weighted integrals over $R^{d}$ for integrands from weighted Sobolev spaces of mixed smoothness. We prove upper and lower bounds of the c…

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★ 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.NA2021★ 1 cited

Collocation approximation by deep neural ReLU networks for parametric elliptic PDEs with lognormal inputs

Dinh Dũng

We obtained convergence rates of the collocation approximation by deep ReLU neural networks of solutions to elliptic PDEs with lognormal inputs, parametrized by $y$ fr…

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.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

Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs

Dinh Dũng

By combining a certain approximation property in the spatial domain, and weighted $ℓ_{2}$ -summability of the Hermite polynomial expansion coefficients in the parametric domain obt…

math.NA2017

$ε$ -dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs

Dinh Dũng, Michael Griebel, Vu Nhat Huy +1

In this article, we present a cost-benefit analysis of the approximation in tensor products of Hilbert spaces of Sobolev-analytic type. The Sobolev part is defined on a finite dime…

math.NA2017

Approximation by translates of a single function of functions in space induced by the convolution with a given function

Dinh Dũng, Charles A. Micchelli, Vu Nhat Huy

We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions…

math.NA2016

B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness

Dinh Dũng

We proved direct and inverse theorems on B-spline quasi-interpolation sampling representation with a Littlewood-Paley-type norm equivalence in Sobolev spaces $W_{p}^{r}$ of mixed smoot…

math.NA2016★ 26 cited

Hyperbolic Cross Approximation

Dinh Dũng, Vladimir N. Temlyakov, Tino Ullrich

Hyperbolic cross approximation is a special type of multivariate approximation. Recently, driven by applications in engineering, biology, medicine and other areas of science new ch…

math.NA2015★ 3 cited

Linear collective collocation and Galerkin approximations for parametric and stochastic elliptic PDEs

Dinh Dũng

Consider the parametric elliptic problem \begin{equation} - \operatorname{dv} \big(a(y)(x)\nabla u(y)(x)\big) \ = \ f(x) \quad x \in D, \ y \in [-1,1]^\infty, \quad u|_{\partial D}…

math.NA2015★ 3 cited

High-dimensional periodic sampling on Smolyak grids based on B-spline quasi-interpolation

Dinh Dũng

We constructed linear algorithms of sampling recovery and cubature formulas on Smolyak grids parametrized by $m \in N$ of periodic $d$ -variate functions having Lipschitz-H…

math.NA2015★ 1 cited

Hyperbolic cross approximation in infinite dimensions

Dinh Dũng, Michael Griebel

We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analyt…

math.CA2014

Kolmogorov n-Widths of Function Classes Induced by a Non-Degenerate Differential Operator: A Convex Duality Approach

Patrick L. Combettes, Dinh Dũng

Let $P (D)$ be the differential operator induced by a polynomial $P$ , and let $U_{2}^{[P]}$ be the class of multivariate periodic functions $f$ such that $∥ P (D) (f) ∥_{2} \leq 1$ . The…

math.NA2014

Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in $H^{γ}$

Glenn Byrenheid, Dinh Dũng, Winfried Sickel +1

We investigate the rate of convergence of linear sampling numbers of the embedding $H^{α, β} (T^{d}) ↪ H^{γ} (T^{d})$ . Here $α$ governs the mixed smoothness…

Local Gevrey regularity and Quasi-Monte Carlo quadrature for PDEs parameterized on non-compact domains

Laguerre- and Laplace-weighted integration of mixed-smoothness functions

Simultaneous spatial-parametric collocation approximation for parametric PDEs with log-normal random inputs

Sampling recovery in Bochner spaces and applications to parametric PDEs

Weighted hyperbolic cross polynomial approximation

Weighted sampling recovery of functions with mixed smoothness

Sparse-grid sampling recovery and numerical integration of functions having mixed smoothness

Numerical weighted integration of functions having mixed smoothness

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

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

Collocation approximation by deep neural ReLU networks for parametric elliptic PDEs with lognormal inputs

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

Deep ReLU neural networks in high-dimensional approximation

Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs

ε-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs

Approximation by translates of a single function of functions in space induced by the convolution with a given function

B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness

Hyperbolic Cross Approximation

Linear collective collocation and Galerkin approximations for parametric and stochastic elliptic PDEs

High-dimensional periodic sampling on Smolyak grids based on B-spline quasi-interpolation

Hyperbolic cross approximation in infinite dimensions

Kolmogorov n-Widths of Function Classes Induced by a Non-Degenerate Differential Operator: A Convex Duality Approach

Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in Hγ

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

$ε$ -dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs

Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in $H^{γ}$