A unified regularization theory: the maximum non-extensive entropy principle



Título del documento: A unified regularization theory: the maximum non-extensive entropy principle
Revista: Computational & applied mathematics
Base de datos: PERIÓDICA
Número de sistema: 000310697
ISSN: 0101-8205
Autores: 1


2
Instituciones: 1Instituto Nacional de Pesquisas Espaciais, Laboratorio Associado de Computacao e Matematica Aplicada, Sao Jose dos Campos, Sao Paulo. Brasil
2Agencia Nacional de Telecomunicacoes, Brasilia, Distrito Federal. Brasil
Año:
Volumen: 25
Número: 2-3
Paginación: 307-330
País: Brasil
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Experimental
Resumen en inglés Tsallis' non-extensive entropy is used as a regularization operator. The parameter ''q'' (non-extensivity parameter) has a central role in the Tsallis' thermostatiscs formalism. Here, several values of q are investigated in inverse problems, using q < 1 and q > 1. Two standard regularization techniques are recovered for special q-values: (i) q = 2 is the well known Tikhonov regularization; (ii) q = 1 is the standard Boltzmann-Gibbs-Shannon formulation for entropy. The regularization feature is illustrated in an inverse test problem: the estimation of initial condition in heat conduction problem. Two methods are studied for determining the regularization parameter, the maximum curvature for the L-curve, and the Morozov's discrepancy principle. The new regularization of higher order is applied to the retrieval of the atmospheric vertical profile from satellite data
Disciplinas: Matemáticas,
Física y astronomía
Palabras clave: Matemáticas aplicadas,
Termodinámica y física estadística,
Entropía,
Teoría de regularización unificada,
Problemas inversos
Keyword: Mathematics,
Physics and astronomy,
Applied mathematics,
Thermodynamics and statistical physics,
Entropy,
Unified regularization theory,
Inverse problems
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