IntervalBoxMap

All of the above techniques provide a fast, efficient way to cover setwise images of boxes, but are not necessarily guaranteed to provide an complete covering. To avoid this as well as other numerical inaccuracies inherent in floating point arithmetic, one can use interval arithmetic to guarantee a rigorous outer covering of box images. Interval arithmetic is a technique from validated numerics which performs calculations while simultaneously recording the error of such calculations. A more detailed discussion and julia-implementation of interval arithmetic can be found in IntervalArithmetic.jl.

BoxMap(:interval, map, domain::Box{N}) -> IntervalBoxMap
BoxMap(:interval, map, domain::Box{N}) -> IntervalBoxMap

Example

julia> F = BoxMap(:interval, f, domain)IntervalBoxMap
julia> p = plot!(
           p, F(B),
           color=RGBA(1.,0.5,0.,0.5),
           lab="interval arithmetic"
       )Plot{Plots.GRBackend() n=4}