%0 Journal Article %T Inner approximation of the range of vector-valued functions %+ Laboratoire d'Informatique de Nantes Atlantique (LINA) %+ Développement des Technologies Nouvelles (DTN) %A Goldsztejn, Alexandre %A Jaulin, Luc %Z WOS %< avec comité de lecture %@ 1385-3139 %J Reliable Computing %I Springer Verlag %P 1-23 %8 2010 %D 2010 %Z Engineering Sciences [physics]/Signal and Image processing %Z Computer Science [cs]/Signal and Image ProcessingJournal articles %X 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. %G English %2 https://hal.science/hal-00518507/document %2 https://hal.science/hal-00518507/file/GoldsztejnJaulinInner2010.pdf %L hal-00518507 %U https://hal.science/hal-00518507 %~ UNIV-NANTES %~ ENSTA-BRETAGNE %~ CNRS %~ LINA %~ ENSTA-BRETAGNE-STIC %~ ENSIETA-E3I2 %~ ENSIETA-DTN %~ NANTES-UNIVERSITE %~ UNIV-NANTES-AV2022