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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 DIIS ： ウィキペディア英語版 DIIS DIIS (direct inversion in the iterative subspace or direct inversion of the iterative subspace), also known as Pulay mixing, is an extrapolation technique. DIIS was developed by Peter Pulay in the field of computational quantum chemistry with the intent to accelerate and stabilize the convergence of the Hartree–Fock self-consistent field method. At a given iteration, the approach constructs a linear combination of approximate error vectors from previous iterations. The coefficients of the linear combination are determined so to best approximate, in a least squares sense, the null vector. The newly determined coefficients are then used to extrapolate the function variable for the next iteration. ==Details== At each iteration, an approximate error vector, , corresponding to the variable value, is determined. After sufficient iterations, a linear combination of previous error vectors is constructed :$\backslash mathbf\; e\_=\backslash sum\_^m\backslash \; c\_i\backslash mathbf\; e\_i.$ The DIIS method seeks to minimize the norm of under the constraint that the coefficients sum to one. The reason why the coefficients must sum to one be can seen if we write the trial vector as the sum of the exact solution () and an error vector. In the DIIS approximation, we get: :$$ \begin \mathbf p &= \sum_i c_i \left( \mathbf p^\text + \mathbf e_i \right) \\ &= \mathbf p^\text \sum_i c_i + \sum_i c_i \mathbf e_i \end We minimize the second term while it is clear that the sum coefficients must be equal to one if we want to find the exact solution. The minimization is done by a Lagrange multiplier technique. Introducing an undetermined multiplier , a Lagrangian is constructed as :$$ \begin L&=\left\|\mathbf e_\right\|^2-\lambda\left(\sum_i\ c_i-1\right),\\ &=\sum_c_jB_c_i-\lambda\left(\sum_i\ c_i-1\right),\text B_=\langle\mathbf e_j, \mathbf e_i\rangle. \end Equating zero to the derivatives of with respect to the coefficients and the multiplier leads to a system of linear equations to be solved for the coefficients (and the Lagrange multiplier). The coefficients are then used to update the variable as :$\backslash mathbf\; p\_=\backslash sum\_^m\; c\_i\backslash mathbf\; p\_i.$ 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「DIIS」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.