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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Padua points ： ウィキペディア英語版 Padua points In polynomial interpolation of two variables, the Padua points are the first known example (and up to now the only one) of a unisolvent point set (that is, the interpolating polynomial is unique) with ''minimal growth'' of their Lebesgue constant, proven to be O(log2 ''n'') .〔 〕 Their name is due to the University of Padua, where they were originally discovered.〔 〕 The points are defined in the domain $\backslash scriptstyle\; ()\backslash times\; ()\backslash subset\; \backslash mathbb^2$. It is possible to use the points with four orientations, obtained with subsequent 90-degree rotations: this way we get four different families of Padua points. == The four families == We can see the Padua point as a "sampling" of a parametric curve, called ''generating curve'', which is slightly different for each of the four families, so that the points for interpolation degree $n$ and family $s$ can be defined as :$\backslash text\_n^s=\backslash lbrace\backslash mathbf=(\backslash xi\_1,\backslash xi\_2)\backslash rbrace=\backslash left\backslash lbrace\backslash gamma\_s\backslash left(\backslash frac\backslash right),k=0,\backslash ldots,n(n+1)\backslash right\backslash rbrace.$ Actually, the Padua points lie exactly on the self-intersections of the curve, and on the intersections of the curve with the boundaries of the square $()^2$. The cardinality of the set $\backslash scriptstyle\; \backslash text\_n^s$ is $\backslash scriptstyle\; |\backslash text\_n^s|=N=\backslash frac$. Moreover, for each family of Padua points, two points lie on consecutive vertices of the square $()^2$, $2n-1$ points lie on the edges of the square, and the remaining points lie on the self-intersections of the generating curve inside the square.〔 〕〔 〕 The four generating curves are ''closed'' parametric curves in the interval $()$, and are a special case of Lissajous curves. 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「Padua points」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.