I need to calculate some fairly complex equations using interval arithmetic. However, the interval width of the final result is too large. I have a feeling that it can be narrowed down especially while performing operations on intervals which have the same underlying parameter. e.g x^2 - x, as x^2 & x are both are dependent on x.
Are there any standard / proven techniques for narrowing down the intervals which can be implemented?
If your function is a combination of elementary functions you need to combine the corresponding (often tight) function enclosures. The combined function enclosure won't be tight generally. You can find tight enclosures of polynomials, for example. But for more complex functions the only way to tighten their enclosures is to subdivide the x-interval.