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I've found many definitions on how to compute the power of an interval, where the power is an integer, but I'd like to find a formula for computing the power more generally.

In other words, I'd like to implement something like the 'pow' method below:

class Interval {
    public final double min;
    public final double max;

    public Interval pow(Interval i) {
        return new Interval(..., ...);
    }
}

In Interval Arithmetic, the standard four operators are relatively straight-forward (read: available on Wikipedia), transcendental functions are not much harder, and integer powers of intervals are not difficult... But interval powers of intervals are throwing me for a loop.

I haven't been able to find any open-source libraries in any language that implement this generalized power function.

I'd appreciate any complete answers, suggestions, and references.

Joshua Warner
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  • This looks straightforward for positive intervals and very hard (undefined?) otherwise... – Nemo Dec 14 '11 at 04:05
  • @Nemo I think that you are right, in that the power function is monotonic if both operands are positive, but I'd like to find something more general, even venturing into the complex realm if necessary. – Joshua Warner Dec 14 '11 at 13:50

0 Answers0