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Using interval arithmetic to prove that a set is path-connected. (English) Zbl 1087.68068
Summary: We give a numerical algorithm able to prove whether a set \(\mathbb S\) described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as \(\mathbb S\). Examples illustrate the principle of the approach.

MSC:
68R10 Graph theory (including graph drawing) in computer science
65G40 General methods in interval analysis
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