IntervalRootFinding.jl
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Test cases
This comes from the (Reliable_computing) mailing list, (posted by Mark A. Stadtherr):
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Minimization problems: http://dx.doi.org/10.1021/ie034073d
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Equation-solving problems (with many roots): http://dx.doi.org/10.1002/aic.690470817
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Other interesting problems/methods by perusing: https://www3.nd.edu/~markst/interval-publications.html