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On the diffusion algorithm for density-equalizing maps with piecewise constant initial data

We mathematically analyze the diffusion-based algorithm to produce maps with a given Jacobian, introduced independently by M. T. Gastner and M. E. J. Newman (2004) and ourselves (2003), but in particular cases where the initial density has line or angle discontinuities in the plane. In this situation, the conclusion reinforces the conjecture that the algorithm is always well-posed, in accordance with its extensive numerical use in some areas of applied sciences (cartograms, sensor networks, computational grids, or image registration)

This work was partially supported by grants from the Spanish Government (MTM2008-06349-C03-01, MTM2011-27739-C04-01, and MTM2011-27739-C04-03) and the Catalan Government (2009SGR345)

info:eu-repo/grantAgreement/MICINN//MTM2011-27739-C04-03/ES/MODELIZACION MATEMATICA, BIOLOGIA TEORICA Y REDES COMPLEJAS/

Wiley

Director: Ministerio de Ciencia e Innovación (Espanya)
Generalitat de Catalunya. Agència de Gestió d’Ajuts Universitaris i de Recerca
Autor: Avinyó Andrés, Albert
Solà-Morales i Rubió, Joan de
València i Guitart, Marta
Data: 15 juliol 2012
Resum: We mathematically analyze the diffusion-based algorithm to produce maps with a given Jacobian, introduced independently by M. T. Gastner and M. E. J. Newman (2004) and ourselves (2003), but in particular cases where the initial density has line or angle discontinuities in the plane. In this situation, the conclusion reinforces the conjecture that the algorithm is always well-posed, in accordance with its extensive numerical use in some areas of applied sciences (cartograms, sensor networks, computational grids, or image registration)
This work was partially supported by grants from the Spanish Government (MTM2008-06349-C03-01, MTM2011-27739-C04-01, and MTM2011-27739-C04-03) and the Catalan Government (2009SGR345)
Format: application/pdf
Accés al document: http://hdl.handle.net/10256/11266
Llenguatge: eng
Editor: Wiley
Col·lecció: info:eu-repo/semantics/altIdentifier/doi/10.1002/mma.2526
info:eu-repo/semantics/altIdentifier/issn/0170-4214
info:eu-repo/semantics/altIdentifier/eissn/1099-1476
AGAUR/2014-2016/2014 SGR-345
És part de: info:eu-repo/grantAgreement/MICINN//MTM2011-27739-C04-03/ES/MODELIZACION MATEMATICA, BIOLOGIA TEORICA Y REDES COMPLEJAS/
Drets: Tots els drets reservats
Matèria: Funcional de densitat, Teoria del
Density functionals
Equacions funcionals
Functional equations
Títol: On the diffusion algorithm for density-equalizing maps with piecewise constant initial data
Tipus: info:eu-repo/semantics/article
Repositori: DUGiDocs

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