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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 Lebesgue constant (interpolation) ： ウィキペディア英語版 Lebesgue constant (interpolation) :''For other uses, see: Lebesgue constant (disambiguation).'' In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the best polynomial approximation of the function (the degree of the polynomials are obviously fixed). The Lebesgue constant for polynomials of degree at most and for the set of nodes is generally denoted by . These constants are named after Henri Lebesgue. ==Definition== We fix the interpolation nodes ''x''0, ..., ''xn'' and an interval (''b'' ) containing all the interpolation nodes. The process of interpolation maps the function ''f'' to a polynomial ''p''. This defines a mapping ''X'' from the space ''C''((''b'' )) of all continuous functions on (''b'' ) to itself. The map ''X'' is linear and it is a projection on the subspace of polynomials of degree or less. The Lebesgue constant is defined as the operator norm of ''X''. This definition requires us to specify a norm on ''C''((''b'' )). The maximum norm is usually the most convenient. 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「Lebesgue constant (interpolation)」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.