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Vincent Lefevre wrote:
>About Remark 5 (and the whole motion), what do the decorations really >mean in practice? For instance, consider f(x) = tan(floor(x)*pi+pi/2), >implemented as the composition of the various basic functions, and its >interval extension. At Level 1, it is ndf for X = [1,1.5], but not at >Level 2, where it is con (because of rounding). With X = [1,3], it is >con at both Level 1 and Level 2, though f(x) is nowhere defined. So, >what confidence con brings here? The decoration con tells you that that the level 2 computation of the function f(x) may have a singularity on the interval x.I meant: what confidence con brings compared to ndf? Since * one can obtain con for a function that is nowhere defined, and * one can obtain ndf for a function that is not nowhere defined (due to the tracking rules), it seems that there isn't a difference between ndf and con.
If one obtains ndf for a function evaluated over interval box X, then one knows with certainty that X is everywhere undefined. This isn't true with con. For example, in branch-and-bound algorithm one can safely delete the box X if it bears the ndf decoration. On the other hand if X bears the decoration con, then X should be i) bisected if a user-specified tolerance has not been met or ii) otherwise marked "indeterminate". In a pathological case like the one you mention above, the branch-and-bound algorithm may bisect the entire input domain to user-specified tolerance and mark all bisected intervals "indeterminate". But in cases not so pathological large subsets of the input domain may be efficiently deleted due to ndf decoration. See, e.g., Section 5.3 of my old DRAFT position paper, attached (and note D2 in that paper is what Motion 27 calls "con"). Nate
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