Publications by Giovanni Migliorati

Function Integration, Reconstruction And Approximation Using Rank-1 Lattices

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 Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...

2021

HE-LHC: The High-Energy Large Hadron Collider Future Circular Collider Conceptual Design Report Volume 4

Pierluigi Bruzzone, Jan Steggemann, Elena Graverini, Jean-Michel Sallese, Thomas Rizzo, Luca Rossi, Leonid Rivkin, Eva Maria Rodriguez Franco, Fabio Avino, Mikhail Chapochnikov

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider ...

2019

FCC Physics Opportunities: Future Circular Collider Conceptual Design Report Volume 1

Pierluigi Bruzzone, Jan Steggemann, Elena Graverini, Jean-Michel Sallese, Thomas Rizzo, Luca Rossi, Rui Ning Wang, Fabio Avino, Xavier Buffat, Tatiana Pieloni

We review the physics opportunities of the Future Circular Collider, covering its e(+)e(-), pp, ep and heavy ion programmes. We describe the measurement capabilities of each FCC component, addressing the study of electroweak, Higgs and strong interactions, ...

2019

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

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⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2022

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

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

2015

Adaptive polynomial approximation by means of random discrete least squares

Giovanni Migliorati

We address adaptive multivariate polynomial approximation by means of the discrete least-squares method with random evaluations, to approximate in the L2 probability sense a smooth function depending on a random variable distributed according to a given pr ...

Springer2015

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Giovanni Migliorati

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is ...

Elsevier2015

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate polynomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated s ...

2015