Article Dans Une Revue Reliable Computing Année : 2010

Inner approximation of the range of vector-valued functions

Résumé

No method for the computation of a reliable subset of the range of vector-valued functions is available today. A method for computing such inner approximations is proposed in the specific case where both domain and co-domain have the same dimension. A general suffi- cient condition for the inclusion of a box inside the image of a box by a continuously differentiable vector-valued is first provided. This sufficient condition is specialized to a more efficient one, which is used in a specific bisection algorithm that computes reliable inner and outer approximations of the image of a domain defined by constraints. Some experimentations are presented.

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hal-00518507 , version 1 (14-01-2011)

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  • HAL Id : hal-00518507 , version 1

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Alexandre Goldsztejn, Luc Jaulin. Inner approximation of the range of vector-valued functions. Reliable Computing, 2010, pp.1-23. ⟨hal-00518507⟩
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