OptimizingFunctionRepresentationsForIntervalAnalysis
Optimizing function representations for interval analysis
MSc thesis project idea, Cezar Ionescu, 2015-03-17
The arithmetical operations on real (or floating-point) numbers can be
easily extended to intervals. For example, adding two intervals I a b
and I c d gives I (a + c) (b + d), or multiplying I a b with a
negative constant alpha < 0 gives I (alpha*b) (alpha*a). A function
that is built out of arithmetical operations is also easily extended,
but sometimes the resulting extension is bad. For example, extending f x = x + (-1*x)
with the previous formulas results in "big" intervals,
instead of just the singleton I 0 0. It would have obviously been
much better to extend the equivalent function f x = 0. Theses in this
area will explore automatic optimization of representations for less
obvious cases.