26 citations · 100 across the 15 of their papers we have counts for
5 papers · 1 filter
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities
Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen +1
We prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in for weighted analytic function classes in certain polytopal domains , in space dimensio…
Weighted analyticity of Hartree-Fock eigenfunctions
Yvon Maday, Carlo Marcati
We prove analytic-type estimates in weighted Sobolev spaces on the eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with singular potentials, which includes…
Low rank tensor approximation of singularly perturbed partial differential equations in one dimension
Carlo Marcati, Maxim Rakhuba, Johan E. M. Ulander
We derive rank bounds on the quantized tensor train (QTT) compressed approximation of singularly perturbed reaction diffusion partial differential equations (PDEs) in one dimension…
p- and hp- virtual elements for the Stokes problem
Alexey Chernov, Carlo Marcati, Lorenzo Mascotto
We analyse the p- and hp-versions of the virtual element method (VEM) for the the Stokes problem on a polygonal domain. The key tool in the analysis is the existence of a bijection…
Analytic regularity for the incompressible Navier-Stokes equations in polygons
Carlo Marcati, Christoph Schwab
In a plane polygon with straight sides, we prove analytic regularity of the Leray-Hopf solution of the stationary, viscous, and incompressible Navier-Stokes equations. We assum…