%0 Journal Article
%T Inner approximation of the range of vector-valued functions
%+ Laboratoire d'Informatique de Nantes Atlantique (LINA)
%+ DÃ©veloppement des Technologies Nouvelles (DTN)
%A Goldsztejn, Alexandre
%A Jaulin, Luc
%Z WOS
%< avec comitÃ© 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