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In mathematics, a subpaving is a set of nonoverlapping box of Rn. A subset ''X'' of R''n'' can be approximated by two subpavings ''X''− and ''X''+ such that ''X''− ⊂ ''X'' ⊂ ''X''+. The three figures on the right show an approximation of the set ''X'' = with different accuracies. The set ''X''− corresponds to red boxes and the set ''X''+ contains all red and yellow boxes. Combined with interval-based methods, subpavings are used to approximate the solution set of non-linear problems such as set inversion problems. 〔 〕 Subpavings can also be used to prove that a set defined by nonlinear inequalities is path connected 〔 〕 , to provide topological properties of such sets 〔 〕 , to solve piano-mover's problems 〔 〕 or to implement set computation 〔 〕 . ==References== 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「subpaving」の詳細全文を読む スポンサード リンク
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