翻訳と辞書 Words near each other ・ Remetea River (Bistra) ・ Remetea River (Olt) ・ Remetea, Bihor ・ Remetea, Harghita ・ Remeteszőlős ・ Remetinec ・ Remetinec prison ・ Remetinec Roundabout ・ Remetinec, Varaždin County ・ Remetovac ・ Remetschwil ・ Remetské Hámre ・ Remexido ・ Remexio Subdistrict ・ Remez algorithm ・ Remez inequality ・ Remezov ・ Remezov Chronicle ・ Remeşin ・ Remeți ・ Remeți Hydroelectric Power Station ・ Remi ・ Remi (disambiguation) ・ Remi A. Balduck ・ Remi Abiola ・ Remi Adefarasin ・ Remi Aubuchon ・ Remi Ayodele ・ Remi Babalola ・ Remi Broadway 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 Remez inequality ： ウィキペディア英語版 Remez inequality In mathematics, the Remez inequality, discovered by the Soviet mathematician Evgeny Yakovlevich Remez , gives a bound on the sup norms of certain polynomials, the bound being attained by the Chebyshev polynomials. ==The inequality== Let σ be an arbitrary fixed positive number. Define the class of polynomials π''n''(σ) to be those polynomials ''p'' of the ''n''th degree for which :$$ |p(x)| \le 1 on some set of measure ≥ 2 contained in the closed interval (). Then the Remez inequality states that :$\backslash sup\_\; \backslash |p\backslash |\_\backslash infty=\backslash |T\_n\backslash |\_\backslash infty$ where ''T''''n''(''x'') is the Chebyshev polynomial of degree ''n'', and the supremum norm is taken over the interval (). Observe that ''T''''n'' is increasing on $(+\backslash infty)$, hence :$\backslash |T\_n\backslash |\_\backslash infty\; =\; T\_n(1+\backslash sigma).$ The R.i., combined with an estimate on Chebyshev polynomials, implies the following corollary: If ''J'' ⊂ R is a finite interval, and ''E'' ⊂ ''J'' is an arbitrary measurable set, then :$\backslash max\_\; |p(x)|\; \backslash leq\; \backslash left(\; \backslash frac\; \backslash right)^n\; \backslash sup\_\; |p(x)|\; \backslash qquad\backslash qquad($ *) for any polynomial ''p'' of degree ''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「Remez 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.