翻訳と辞書 Words near each other ・ Whitney Hedgepeth ・ Whitney High School ・ Whitney High School (Cerritos, California) ・ Whitney High School (Rocklin, California) ・ Whitney High School (Toledo, Ohio) ・ Whitney Hillier ・ Whitney Hills ・ Whitney House ・ Whitney Houston ・ Whitney Houston (album) ・ Whitney Houston chart records and achievements ・ Whitney Houston discography ・ Whitney Houston videography ・ Whitney immersion theorem ・ Whitney Independent School District ・ Whitney inequality ・ Whitney Institute Middle School ・ Whitney Joins The JAMs ・ Whitney Jones ・ Whitney K. Newey ・ Whitney Kershaw ・ Whitney Keyes ・ Whitney Kroenke Burditt ・ Whitney L. Van Cleve ・ Whitney Laboratory for Marine Bioscience ・ Whitney Lakes Provincial Park ・ Whitney Lewis ・ Whitney M. Young Gifted & Talented Leadership Academy ・ Whitney M. Young Magnet High School ・ Whitney MacMillan Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Whitney inequality ： ウィキペディア英語版 Whitney inequality In mathematics, the Whitney inequality gives an upper bound for the error of best approximation of a function by polynomials in terms of the moduli of smoothness. It was first proved by Hassler Whitney in 1957, and is an important tool in the field of approximation theory for obtaining upper estimates on the errors of best approximation. ==Statement of the theorem== Denote the value of the best uniform approximation of a function $f\backslash in\; C(())$ by algebraic polynomials $P\_n$ of degree $\backslash leq\; n$ by : $E\_n(f)\_\; :=\; \backslash inf\_\; \backslash |\backslash Delta\_h^k(f;\backslash cdot)\backslash |\_\; \backslash quad\; \backslash text\; \backslash quad\; t\backslash in\; (),$ : $\backslash omega\_k(t):=\backslash omega\_k((b-a)/k)\backslash quad\; \backslash text\; \backslash quad\; t>(b-a)/k\; ,$ where $\backslash Delta\_h^k$ is the finite difference of order $k$. Theorem: (1957 ) If $f\backslash in\; C(())$, then : $E\_(f)\_\backslash leq\; W\_k\; \backslash omega\_k\backslash left(\backslash frac;f;()\backslash right)$ where $W\_k$ is a constant depending only on $k$. The Whitney constant $W(k)$ is the smallest value of $W\_k$ for which the above inequality holds. The theorem is particularly useful when applied on intervals of small length, leading to good estimates on the error of spline approximation. 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「Whitney inequality」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.