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 continuousversion 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.
A gradient flow approach to quantization of measures / Caglioti, Emanuele; Francois, Golse; Iacobelli, Mikaela. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 10:25(2015), pp. 1845-1885. [10.1142/S0218202515500475]
A gradient flow approach to quantization of measures
CAGLIOTI, Emanuele;IACOBELLI, MIKAELA
2015
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 continuousversion 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.| File | Dimensione | Formato | |
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