G. Migliorati

activity

20182021

collaborators

5 papers

math.NA2021

Near-optimal approximation methods for elliptic PDEs with lognormal coefficients

Albert Cohen, Giovanni Migliorati

This paper studies numerical methods for the approximation of elliptic PDEs with lognormal coefficients of the form $- div (a \nabla u) = f$ where $a = exp (b)$ and $b$ is a Gaussia…

math.NA2019

Function integration, reconstruction and approximation using rank-1 lattices

Frances Y. Kuo, Giovanni Migliorati, Fabio Nobile +1

We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fo…

math.NA2019

Multivariate approximation of functions on irregular domains by weighted least-squares methods

Giovanni Migliorati

We propose and analyse numerical algorithms based on weighted least squares for the approximation of a real-valued function on a general bounded domain $Ω \subset R^{d}$ . Giv…

math.NA2018

Stable high-order randomized cubature formulae in arbitrary dimension

Giovanni Migliorati, Fabio Nobile

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure $μ$ defined on a domain $Γ\subseteq \math…

math.NA2018

Adaptive approximation by optimal weighted least squares methods

Giovanni Migliorati

Given any domain $X \subseteq R^{d}$ and a probability measure $ρ$ on $X$ , we study the problem of approximating in $L^{2} (X, ρ)$ a given function $u : X \to R$ , using its…