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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 Discrete Chebyshev polynomials ： ウィキペディア英語版 Discrete Chebyshev polynomials In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced by and rediscovered by . ==Definition== The polynomials are defined as follows: Let ''f'' be a smooth function defined on the closed interval (), whose values are known explicitly only at points ''x''''k'' := −1 + (2''k'' − 1)/''m,'' where ''k'' and ''m'' are integers and 1 ≤ ''k'' ≤ ''m''. The task is to approximate ''f'' as a polynomial of degree ''n'' < ''m''. Consider a positive semi-definite bilinear form :$\backslash left(g,h\backslash right)\_d:=\backslash frac\backslash sum\_^,$ where ''g'' and ''h'' are continuous on () and let :$\backslash left\backslash |g\backslash right\backslash |\_d:=(g,g)^\_$ be a discrete semi-norm. Let φ''k'' be a family of polynomials orthogonal to each other :$\backslash left(\; \backslash phi\_k,\; \backslash phi\_i\backslash right)\_d=0$ whenever i is not equal to k. Assume all the polynomials φ''k'' have a positive leading coefficient and they are normalized in such a way that :$\backslash left\backslash |\backslash phi\_k\backslash right\backslash |\_d=1.$ The φ''k'' are called discrete Chebyshev (or Gram) polynomials. 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「Discrete Chebyshev polynomials」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.