Matthieu Dolbeault

activity

20202026

most citedA sharp upper bound for sampling numbers in

L_{2}

53 citations · 92 across the 8 of their papers we have counts for

collaborators

8 papers

math.NA2026

Constructive discretization and approximation in reproducing kernel Hilbert spaces

Abdellah Chkifa, Matthieu Dolbeault, David Krieg +1

We generalize the sparsification algorithm of Batson, Spielman and Srivastava, making one part of the result dimension-independent. In particular, we recover discretization inequal…

cs.LG2024

State estimation of urban air pollution with statistical, physical, and super-learning graph models

Matthieu Dolbeault, Olga Mula, Agustín Somacal

We consider the problem of real-time reconstruction of urban air pollution maps. The task is challenging due to the heterogeneous sources of available data, the scarcity of direct…

math.NA2023★ 1 cited

Randomized least-squares with minimal oversampling and interpolation in general spaces

Abdellah Chkifa, Matthieu Dolbeault

In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that…

math.AP2023

Reduced order modeling for elliptic problems with high contrast diffusion coefficients

Albert Cohen, Matthieu Dolbeault, Agustin Somacal +1

We consider the parametric elliptic PDE $- div (a (y) \nabla u) = f$ on a spatial domain $Ω$ , with $a (y)$ a scalar piecewise constant diffusion coefficient taking any positive val…

math.NA2022

Nonlinear approximation spaces for inverse problems

Albert Cohen, Matthieu Dolbeault, Olga Mula +1

This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements possibly affected by noise. In recent years, inversi…

math.NA2022★ 53 cited

A sharp upper bound for sampling numbers in $L_{2}$

Matthieu Dolbeault, David Krieg, Mario Ullrich

For a class $F$ of complex-valued functions on a set $D$ , we denote by $g_{n} (F)$ its sampling numbers, i.e., the minimal worst-case error on $F$ , measured in $L_{2}$ , that can be achi…

math.NA2021★ 38 cited

Optimal pointwise sampling for $L^{2}$ approximation

Albert Cohen, Matthieu Dolbeault

Given a function $u \in L^{2} = L^{2} (D, μ)$ , where $D \subset R^{d}$ and $μ$ is a measure on $D$ , and a linear subspace $V_{n} \subset L^{2}$ of dimension $n$ , we show that near-best appr…

math.NA2020

Optimal sampling and Christoffel functions on general domains