Abstract
In many interval computation methods, if we cannot guarantee a solution within a given interval, it often makes sense to "inflate" this interval a little bit. There exist many different "inflation" methods. The authors of PASCAL-XSC, after empirically comparing the behavior of different inflation methods, decided to implement the formula [x-,x+]e = [(1 + e)x- - e · x+, (1 + e)x+ - e · x-]. A natural question is: Is this choice really optimal (in some reasonable sense), or is it only an empirical approximation to the truly optimal choice?
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