Project : coprin
Section: New Results
Keywords : modal intervals, generalized intervals, AE-solution set.
Participant : Alexandre Goldsztejn.
Modal intervals and AE-solution sets
We have proposed an algorithm to compute inner and outer approximations of a linear All Exists (AE)-solution set under the form of skew boxes, i.e. hyper-parallelograms. This algorithm has two advantages:
skew boxes are more general than boxes, therefore the exact AE-solution sets is more accurately approximated by skew boxes than by boxes
convergence of the inner approximation operator is drastically improved by the introducing a post-conditioning ( or "right-preconditioning" ).
An article has been submitted to the journal Reliable Computing.
Modal intervals theory
In our thesis, that shall soon be defended, we introduce a reformulation of modal intervals theory. This reformulation includes the main results of modal intervals theory and proposes a new extension, the Taylor AE-extension.