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In the past I used the function bound_taylor1 (already in TaylorModels.jl) to achieve tighter bounds, but since then IntervalRootFinding.jl has changed a bit, and the methods I introduced are certainly out of date.
This is what is implemented in IntervalOptimization.jl, although there will be some details to sort out to make it workable for e.g. > 2 variables. Also, at the moment it is difficult to make it stop in particular circumstances.
The idea is to have other methods to improve bounding polynomials, specially with many variables.
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