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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 Bernstein polynomial ： ウィキペディア英語版 Bernstein polynomial In the mathematical field of numerical analysis, a Bernstein polynomial, named after Sergei Natanovich Bernstein, is a polynomial in the Bernstein form, that is a linear combination of Bernstein basis polynomials. A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm. Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Stone–Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted to the interval (), became important in the form of Bézier curves. ==Definition== The ''n'' + 1 Bernstein basis polynomials of degree ''n'' are defined as : $b\_(x)\; =\; x^\; \backslash left(\; 1\; -\; x\; \backslash right)^,\; \backslash quad\; \backslash nu\; =\; 0,\; \backslash ldots,\; n.$ where $$ is a binomial coefficient. The Bernstein basis polynomials of degree ''n'' form a basis for the vector space Π''n'' of polynomials of degree at most ''n''. A linear combination of Bernstein basis polynomials :$B\_n(x)\; =\; \backslash sum\_^\; \backslash beta\_\; b\_(x)$ is called a Bernstein polynomial or polynomial in Bernstein form of degree ''n''. The coefficients $\backslash beta\_\backslash nu$ are called Bernstein coefficients or Bézier coefficients. 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「Bernstein polynomial」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.