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Re: IEEE standard for interval arithmetic approved

From: Oliver Heimlich
Subject: Re: IEEE standard for interval arithmetic approved
Date: Fri, 12 Jun 2015 17:44:56 +0200
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Icedove/31.7.0

On 12.06.2015 10:25, Alexander Barth wrote:
Dear Oliver,

Thank you providing this package! I have to say, that I was not aware of
interval arithmetic before and I think that it can be a very useful way
to describe the uncertainties of e.g. models.

I have just a basic questions about discontinuous functions. For example

 >> tan(infsup(1.4,1.7))
ans = [Entire]

I would expect [tan(1.4), ∞[ ∪ ]-∞, tan(1.7)]. Does the interval
arithmetic reduce the results always to a simple interval?


yes, this is the standard behaviour. The result of interval arithmetic operations is always an interval. Otherwise you would have to handle sets of disjoint intervals, which is not provided by this implementation.

There is also one exception to this rule: Reverse multiplication [1], a.k.a. two-output division, can split the result into two intervals. Also there are some set operations [2], which provide similar functionality.

If you use decorated intervals [3], you can see from the result whether your function has been evaluated for inputs where it is discontinuous or undefined. Simply don't use “infsup”, but any other interval constructor for that feature.

[1] http://octave.sourceforge.net/interval/function/@infsup/mulrev.html
[2] http://octave.sourceforge.net/interval/function/@infsup/setxor.html
[3] http://octave.sourceforge.net/interval/package_doc/Advanced-Topics.html#Decorations

I any case, thank you for sharing your work!
> Alex

Thanks for using it and providing feedback :-)


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