G. Migliorati

activity

20152021

most citedAdaptive approximation by optimal weighted least squares methods

2 citations · 4 across the 6 of their papers we have counts for

collaborators

11 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★ 1 cited

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★ 2 cited

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…

math.NA2016

Multivariate approximation in downward closed polynomial spaces

Albert Cohen, Giovanni Migliorati

The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is lar…

math.NA2016★ 1 cited

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Albert Cohen, Giovanni Migliorati, Fabio Nobile

We analyze the accuracy of the discrete least-squares approximation of a function $u$ in multivariate polynomial spaces $P_{Λ} := span {y \mapsto y^{ν} : ν \in Λ}$ wit…

math.NA2016

Optimal weighted least-squares methods

Albert Cohen, Giovanni Migliorati

We consider the problem of reconstructing an unknown bounded function $u$ defined on a domain $X \subset R^{d}$ from noiseless or noisy samples of $u$ at $n$ points $(x^i)_{i…

math.NA2016

Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients

Markus Bachmayr, Albert Cohen, Giovanni Migliorati

Approximation of elliptic PDEs with random diffusion coefficients typically requires a representation of the diffusion field in terms of a sequence $y = (y_{j})_{j \geq 1}$ of scalar ra…

math.NA2015

Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients

Markus Bachmayr, Albert Cohen, Ronald DeVore +1

Elliptic partial differential equations with diffusion coefficients of lognormal form, that is $a = e x p (b)$ , where $b$ is a Gaussian random field, are considered. We study the $\ell^…

math.NA2015

Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients

Markus Bachmayr, Albert Cohen, Giovanni Migliorati

We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial…