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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 Krylov subspace ： ウィキペディア英語版 Krylov subspace In linear algebra, the order-''r'' Krylov subspace generated by an ''n''-by-''n'' matrix ''A'' and a vector ''b'' of dimension ''n'' is the linear subspace spanned by the images of ''b'' under the first ''r'' powers of ''A'' (starting from $A^0=I$), that is, ::$\backslash mathcal\_r(A,b)\; =\; \backslash operatorname\; \backslash ,\; \backslash .\; \backslash ,$ ==Background== The concept is named after Russian applied mathematician and naval engineer Alexei Krylov, who published a paper about it in 1931. The basis for the Krylov subspace is derived from the Cayley–Hamilton theorem which implies that the inverse of a matrix can be found in terms of a linear combination of its powers.〔(【引用サイトリンク】title=A.N.Krylov, a short biography )6 Dec. 2012.〕〔Grigorian, A. T. (2008). ("Krylov, Aleksei Nikolaevich." ) Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. 6 Dec. 2012.〕 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「Krylov subspace」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.