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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1845-1885
Number of pages	41
Journal	Mathematical Models and Methods in Applied Sciences
Volume	25
Issue number	10
DOIs	https://doi.org/10.1142/S0218202515500475
Publication status	Published - 20 Sept 2015

Keywords

Monge-Kantorovich distance
Quantization of measures
gradient flow
parabolic equation

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10.1142/S0218202515500475

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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.",

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AU - Iacobelli, Mikaela

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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.

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KW - Quantization of measures

KW - gradient flow

KW - parabolic equation

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A gradient flow approach to quantization of measures

Abstract

Keywords

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