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That's great. Interval arithmetic is an underappreciated area of study, not because it's particularly difficult - anyone can grasp it in short order, but it's r
by kelseyfrog 4y ago
That's great. Interval arithmetic is an underappreciated area of study, not because it's particularly difficult - anyone can grasp it in short order, but it's rarely the first, second, or third tool used for the job when confronted with a problem. Perhaps it's just not prestigious enough compared to more sophisticated methods.
- 6gvONxR4sf7o 4y agoHow does this generally work in high dimensions? In 1d, an interval is a really simple thing. In higher dimensions, it generalizes in a bunch of ways, from a box to an arbitrary convex region. Given that practical problems tend to have the interesting bits constrained around a lower dimensional region, I imagine that the wrong representations (e.g. just an axis-aligned box) could make the intervals meaningless. Is that the case? Is it simple to overcome that (e.g. just align the box along the interesting subspace), or in practice is it harder to have useful high dimensional "intervals?"