A gradient flow approach to quantization of measures

Emanuele Caglioti; François Golse; Mikaela Iacobelli

doi:10.1142/S0218202515500475

A gradient flow approach to quantization of measures

Emanuele Caglioti
, François Golse
, Mikaela Iacobelli

University of Rome

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

In this paper we study a gradient flow approach to the problem of quantization of measures in space dimension one. By embedding our problem in L², we find a continuous version of this problem corresponding to the limit as the number of atoms in the approximating measure tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence results for the discrete and continuous dynamics.

langue originale	Anglais
Pages (de - à)	1845-1885
Nombre de pages	41
journal	Mathematical Models and Methods in Applied Sciences
Volume	25
Numéro de publication	10
Les DOIs	https://doi.org/10.1142/S0218202515500475
état	Publié - 20 sept. 2015

Accès au document

10.1142/S0218202515500475

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

@article{b4fd94189e124d49931d6d8a5fdf1433,

title = "A gradient flow approach to quantization of measures",

abstract = "In this paper we study a gradient flow approach to the problem of quantization of measures in space dimension one. By embedding our problem in L2, we find a continuous version of this problem corresponding to the limit as the number of atoms in the approximating measure tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence results for the discrete and continuous dynamics.",

keywords = "Monge-Kantorovich distance, Quantization of measures, gradient flow, parabolic equation",

author = "Emanuele Caglioti and Fran{\c c}ois Golse and Mikaela Iacobelli",

note = "Publisher Copyright: {\textcopyright} 2015 World Scientific Publishing Company.",

year = "2015",

month = sep,

day = "20",

doi = "10.1142/S0218202515500475",

language = "English",

volume = "25",

pages = "1845--1885",

journal = "Mathematical Models and Methods in Applied Sciences",

issn = "0218-2025",

number = "10",

}

TY - JOUR

T1 - A gradient flow approach to quantization of measures

AU - Caglioti, Emanuele

AU - Golse, François

AU - Iacobelli, Mikaela

PY - 2015/9/20

Y1 - 2015/9/20

N2 - In this paper we study a gradient flow approach to the problem of quantization of measures in space dimension one. By embedding our problem in L2, we find a continuous version of this problem corresponding to the limit as the number of atoms in the approximating measure tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence results for the discrete and continuous dynamics.

AB - In this paper we study a gradient flow approach to the problem of quantization of measures in space dimension one. By embedding our problem in L2, we find a continuous version of this problem corresponding to the limit as the number of atoms in the approximating measure tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence results for the discrete and continuous dynamics.

KW - Monge-Kantorovich distance

KW - Quantization of measures

KW - gradient flow

KW - parabolic equation

UR - https://www.scopus.com/pages/publications/84941874298

U2 - 10.1142/S0218202515500475

DO - 10.1142/S0218202515500475

M3 - Article

AN - SCOPUS:84941874298

SN - 0218-2025

VL - 25

SP - 1845

EP - 1885

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 10

ER -

A gradient flow approach to quantization of measures

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Contient cette citation