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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 Chebyshev nodes ： ウィキペディア英語版 Chebyshev nodes In numerical analysis, Chebyshev nodes are the roots of the Chebyshev polynomial of the first kind, which are algebraic numbers. They are often used as nodes in polynomial interpolation because the resulting interpolation polynomial minimizes the effect of Runge's phenomenon. ==Definition== For a given natural number ''n'', Chebyshev nodes in the interval (−1, 1) are :$x\_k\; =\; \backslash cos\backslash left(\backslash frac\backslash pi\backslash right)\; \backslash mbox\; k=1,\backslash ldots,n.$ These are the roots of the Chebyshev polynomial of the first kind of degree n. For nodes over an arbitrary interval (''b'' ) an affine transformation can be used: :$\_k\; =\; \backslash frac\; (a+b)\; +\; \backslash frac\; (b-a)\; \backslash cos\backslash left(\backslash frac\backslash pi\backslash right)\; \backslash mbox\; k=1,\; \backslash ldots,\; n.$ 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「Chebyshev nodes」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.