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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 Eigenvalues and eigenvectors of the second derivative ： ウィキペディア英語版 Eigenvalues and eigenvectors of the second derivative Explicit formulas for eigenvalues and eigenvectors of the second derivative with different boundary conditions are provided both for the continuous and discrete cases. In the discrete case, the standard central difference approximation of the second derivative is used on a uniform grid. These formulas are used to derive the expressions for eigenfunctions of Laplacian in case of separation of variables, as well as to find eigenvalues and eigenvectors of multidimensional discrete Laplacian on a regular grid, which is presented as a Kronecker sum of discrete Laplacians in one-dimension. ==The continuous case== The index j represents the jth eigenvalue or eigenvector and runs from 1 to $\backslash infty$. Assuming the equation is defined on the domain $x\; \backslash in\; ()$, the following are the eigenvalues and normalized eigenvectors. The eigenvalues are ordered in descending order. 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「Eigenvalues and eigenvectors of the second derivative」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.