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In mathematics, an interval contractor (or contractor for short) 〔 〕 associated to a set ''X'' is an operator ''C'' which associates to a box () in R''n'' another box ''C''(()) of R''n'' such that the two following properties are always satisfied * C(())\subset () (contractance property) * C(())\cap X=()\cap X (completeness property) A ''contractor associated to a constraint'' (such as an equation or an inequality) is a contractor associated to the set ''X'' of all ''x'' which satisfy the constraint. Contractors make it possible to improve the efficiency of branch-and-bound algorithms classically used in interval analysis. ==Properties of contractors== A contractor ''C'' is monotonic if we have () \subset () \Rightarrow C(())\subset C(()) It is ''minimal'' if for all boxes (), we have C(())=()\cap X] , where () is the ''interval hull'' of the set ''A'', i.e., the smallest box enclosing ''A''. The contractor ''C'' is ''thin'' if for all points ''x'', C(\)=\\cap X where denotes the degenerated box enclosing ''x'' as a single point. The contractor ''C'' is ''idempotent'' if for all boxes (), we have C \circ C(()) = C(()). The contractor ''C'' is ''convergent'' if for all sequences ()(''k'') of boxes containing ''x'', we have ()(k)\rightarrow x \Rightarrow C(()(k))\rightarrow \\cap X. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Interval contractor」の詳細全文を読む スポンサード リンク
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