interval arithmetic

Let it all hang out

interval arithmetic

PostPosted by drab » Tue Nov 22, 2016 3:54 pm

I just love the rational arithmetic.

A possible new companion to it might be interval arithmetic.

While it might be a little tricky to implement in some areas, it would be really fascinating. And it could be extraordinarily useful for error analysis.

An interval number would have 2 parts -- a minimum value and a maximum value. We're running out of syntactic joining characters, but perhaps d could be used for interval Delta. For example, 1.0d1.3 would mean a number of about 1.2, with a possible error range of 0.3.

The parts would propagate through all calculations, and perhaps the gap would get wider, indicating a growing uncertainty.

There are some interesting ramifications, too.
For example, an argument could be made that
0÷0 ←→ ¯∞d∞
and that constant might have the nickname of Anything.
drab
 
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Re: interval arithmetic

PostPosted by forummaster » Wed Nov 23, 2016 5:29 pm

Nice idea. There is already a library called Arb (http://arblib.org/) to support multi-precision ball arithmetic.
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