In this paper, we focus on the inverseproblem associated with a DE: Given a target function x, find a DE such that its solution View the MathML source is sufficiently close to x in the sup norm distance. We extend the previous method for solvinginverseproblems for DEs using the Collage Theorem along a new direction. We search for a set of coefficients that not only minimizes the collage error but also maximizes the entropy. This approach is motivated by some promising results for IFS and probabilities. In our new formulation, the minimization of the collage error can be understood as a multi-criteria problem: two different and conflicting criteria are considered, i.e., collage error and the entropy. In order to deal with this kind of scenario we propose to scalarize the model, which reduces the multi-criteria program to a single-criteria program by combining all objective functions with different trade-off weights. Numerical examples confirm the sub-optimality of the collage theorem and we show that, by adding the entropy term, we obtain a better approximation of the solution

Solving inverse problems for DEs using the collage theorem and entropy maximization / H. Kunze, D. la Torre, E.R. Vrscay. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - 25:12(2012), pp. 2306-2311.

Solving inverse problems for DEs using the collage theorem and entropy maximization

D. la Torre
Secondo
;
2012

Abstract

In this paper, we focus on the inverseproblem associated with a DE: Given a target function x, find a DE such that its solution View the MathML source is sufficiently close to x in the sup norm distance. We extend the previous method for solvinginverseproblems for DEs using the Collage Theorem along a new direction. We search for a set of coefficients that not only minimizes the collage error but also maximizes the entropy. This approach is motivated by some promising results for IFS and probabilities. In our new formulation, the minimization of the collage error can be understood as a multi-criteria problem: two different and conflicting criteria are considered, i.e., collage error and the entropy. In order to deal with this kind of scenario we propose to scalarize the model, which reduces the multi-criteria program to a single-criteria program by combining all objective functions with different trade-off weights. Numerical examples confirm the sub-optimality of the collage theorem and we show that, by adding the entropy term, we obtain a better approximation of the solution
Collage Theorem; Entropy; Inverse problems for DEs
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/05 - Analisi Matematica
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/178439
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