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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 quadratic eigenvalue problem ： ウィキペディア英語版 quadratic eigenvalue problem In mathematics, the quadratic eigenvalue problem〔F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Rev., 43 (2001), pp. 235–286.〕 (QEP), is to find scalar eigenvalues $\backslash lambda\backslash ,$, left eigenvectors $y\backslash ,$ and right eigenvectors $x\backslash ,$ such that :$Q(\backslash lambda)x\; =\; 0\backslash texty^\backslash ast\; Q(\backslash lambda)\; =\; 0,\backslash ,$ where $Q(\backslash lambda)=\backslash lambda^2\; A\_2\; +\; \backslash lambda\; A\_1\; +\; A\_0\backslash ,$, with matrix coefficients $A\_2,\; \backslash ,\; A\_1,\; A\_0\; \backslash in\; \backslash mathbb^$ and we require that $A\_2\backslash ,\backslash neq\; 0$, (so that we have a nonzero leading coefficient). There are $2n\backslash ,$ eigenvalues that may be ''infinite'' or finite, and possibly zero. This is a special case of a nonlinear eigenproblem. $Q(\backslash lambda)$ is also known as a quadratic matrix polynomial. ==Applications== A QEP can result in part of the dynamic analysis of structures discretized by the finite element method. In this case the quadratic, $Q(\backslash lambda)\backslash ,$ has the form $Q(\backslash lambda)=\backslash lambda^2\; M\; +\; \backslash lambda\; C\; +\; K\backslash ,$, where $M\backslash ,$ is the mass matrix, $C\backslash ,$ is the damping matrix and $K\backslash ,$ is the stiffness matrix. Other applications include vibro-acoustics and fluid dynamics. 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「quadratic eigenvalue problem」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.