F. Piazzon

activity

20132025

most citedOptimal Polynomial Admissible Meshes on Some Classes of Compact Subsets of

R^{d}

1 citations · 1 across the 9 of their papers we have counts for

collaborators

14 papers

math.NA2025

The Lebesgue constant for uniform approximation of differential forms

Ludovico Bruni Bruno, Fwderico Piazzon

In this work we address the problem of uniform approximation of differential forms starting from weak data defined by integration on rectifiable sets. We study approximation scheme…

math.NA2023

Computing the L1 optimal transport density: a FEM approach

Federico Piazzon, Enrico Facca, Mario Putti

The $L^{1}$ optimal transport density $μ^{*}$ is the unique $L^{\infty}$ solution of the Monge-Kantorovich equations. It has been recently characterized also as the unique minimizer of t…

math.NA2022

Computing optimal experimental designs on finite sets by log-determinant gradient flow

Federico Piazzon

Optimal experimental designs are probability measures with finite support enjoying an optimality property for the computation of least squares estimators. We present an algorithm f…

math.CV2020

Correction/Addendum to "The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation"

T. Bloom, L. Bos, N. Levenberg +2

We correct the calculation of the Monge-Ampère measure of a certain extremal plurisubharmonic function for the complex Euclidean ball in C^2.

math.AP2019

Transport Energy

Enrico Facca, Federico Piazzon

We introduce the \emph{transport energy} functional $E$ (a variant of the Bouchitté-Buttazzo-Seppecher shape optimization functional) and we prove that its unique minimize…

math.CV2018

The extremal plurisubharmonic function of the torus

Federico Piazzon

We compute the extremal plurisubharmonic function of the real torus viewed as a compact subset of its natural algebraic complexification.

math.CV2018

The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation

T. Bloom, L. Bos, N. Levenberg +2

We discuss the Siciak-Zaharjuta extremal function of pluripotential theory for the unit ball in C^d for spaces of polynomials with the notion of degree determined by a convex body…

math.NA2017

Pluripotential Numerics

Federico Piazzon

We introduce numerical methods for the approximation of the main (global) quantities in Pluripotential Theory as the \emph{extremal plurisubharmonic function} $V_{E}^{*}$ of a compact…

math.SP2017

Laplace Beltrami operator in the Baran metric and pluripotential equilibrium measure: the ball, the simplex and the sphere

Federico Piazzon

The Baran metric $δ_{E}$ is a Finsler metric on the interior of $E \subset R^{n}$ arising from Pluripotential Theory. We consider the few instances, namely $E$ being the ball, the simp…

math.NA2016

Caratheodory-Tchakaloff Subsampling

Federico Piazzon, Alvise Sommariva, Marco Vianello

We present a brief survey on the compression of discrete measures by Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic Programming and the application…

math.CV2015

A weighted extremal function and equilibrium measure

Len Bos, Norman Levenberg, Sione Ma`u +1

Let $K = R^{n} \subset C^{n}$ and $Q (x) := \frac{1}{2} lo g (1 + x^{2})$ where $x = (x_{1}, ..., x_{n})$ and $x^{2} = x_{1}^{2} + \dots + x_{n}^{2}$ . Utilizing extremal functions for convex bodies in ${…

math.CA2015

An Orthogonality Property of the Legendre Polynomials

Len Bos, Akil Narayan, Norm Levenberg +1

We give a remarkable additional orthogonality property of the classical Legendre polynomials on the real interval $[- 1, 1]$ : polynomials up to degree $n$ from this family are mutual…

math.CV2015

Some results on the rational Bernstein Markov property in the complex plane

Federico Piazzon

The Bernstein Markov Property, shortly BMP, is an asymptotic quan- titative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with res…

math.NA2013★ 1 cited

Optimal Polynomial Admissible Meshes on Some Classes of Compact Subsets of $R^{d}$

Federico Piazzon

We show that any compact subset of $R^{d}$ which is the closure of a bounded star-shaped Lipschitz domain $Ω$ , such that $∁ Ω$ has positive reach in the sense of Federer,…

The Lebesgue constant for uniform approximation of differential forms

Computing the L1 optimal transport density: a FEM approach

Computing optimal experimental designs on finite sets by log-determinant gradient flow

Correction/Addendum to "The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation"

Transport Energy

The extremal plurisubharmonic function of the torus

The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation

Pluripotential Numerics

Laplace Beltrami operator in the Baran metric and pluripotential equilibrium measure: the ball, the simplex and the sphere

Caratheodory-Tchakaloff Subsampling

A weighted extremal function and equilibrium measure

An Orthogonality Property of the Legendre Polynomials

Some results on the rational Bernstein Markov property in the complex plane

Optimal Polynomial Admissible Meshes on Some Classes of Compact Subsets of Rd

Optimal Polynomial Admissible Meshes on Some Classes of Compact Subsets of $R^{d}$