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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's inequality (mathematical analysis) ： ウィキペディア英語版 Bernstein's inequality (mathematical analysis) In mathematical analysis, Bernstein's inequality is named after Sergei Natanovich Bernstein. The inequality states that on the complex plane, within the disk of radius 1, the degree of a polynomial times the maximum value of a polynomial is an upper bound for the similar maximum of its derivative. ==Theorem== Let ''P'' be a polynomial of degree $n$ on complex numbers with derivative ''P′''. Then :$\backslash max\_(\; |P\text{'}(z)|\; )\; \backslash le\; n\backslash cdot\backslash max\_(\; |P(z)|\; )$ The inequality finds uses in the field of approximation theory. Using the Bernstein's inequality we have for the ''k'':th derivative, :$\backslash max\_(\; |P^(z)|\; )\; \backslash le\; \backslash frac\; \backslash cdot\backslash max\_(\; |P(z)|\; ).$ 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's inequality (mathematical analysis)」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.