3

From the Section 3.1 of this paper

The Dependency Problem. The main downside of interval arithmetic is that the computed bounds may be extremely pessimistic. As an example, consider the simple operation ← 2 −, evaluated on the range ∈ [−1, 1]. Clearly the actual bound on is [−1, 1], but applying the rules above yields a looser bound of [−1, 2] even in this simple example.

When I try to apply Interval Arithmetic rules I get:

$$f([-1, 1]) = [min(-2, 2), max(-2, 2)] + -1 [-1, 1] = [-2, 2] + [-1, 1] = [-3, 3]$$

I do see that this yields a looser bound but I don't understand why it becomes $[-1, 2]$

Cedric Martens
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    I suspect this is just a typo, but since I'm not an expert I'm going to hold off on posting that as an answer. – Noah Schweber Jun 12 '23 at 18:34
  • I have emailed the author and he confirmed it was a typo. I will be closing this question – Cedric Martens Jun 13 '23 at 03:19
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    I have emailed the author and he has confirmed it is a typo. Therefore, this question has no point. – Cedric Martens Jun 13 '23 at 03:19
  • Yes , I had come to the typo conclusion , which it is immaterial in Present Case , because the Author is skipping it , to move on to more accurate Method. The Correction & the typo have no value except to state that the Method is inaccurate. – Prem Jun 13 '23 at 06:07

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