翻訳と辞書 Words near each other ・ Davie Colquhoun ・ Davie Cooper ・ Davie County Courthouse ・ Davidka ・ Davidka Square ・ Davidka Square bus bombing ・ Davidkovo ・ Davido ・ Davidof Island ・ Davidof Volcano ・ Davidoff ・ Davidoff (disambiguation) ・ Davidoff (surname) ・ Davidoglu ・ Davidon ・ Davidon–Fletcher–Powell formula ・ Davidov ・ Davidov (municipality) ・ Davidov Spur ・ Davidov Stradivarius ・ Davidovac ・ Davidovac, Kladovo ・ Davidovac, Paraćin ・ Davidovac, Svrljig ・ Davidovac, Vranje ・ Davidovica ・ Davidovich ・ Davidovich Bagels ・ Davidovici ・ Davidovka Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Davidon–Fletcher–Powell formula ： ウィキペディア英語版 Davidon–Fletcher–Powell formula The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition (see below). It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix. Given a function $f(x)$, its gradient ($\backslash nabla\; f$), and positive definite Hessian matrix $B$, the Taylor series is: :$f(x\_k+s\_k)=f(x\_k)+\backslash nabla\; f(x\_k)^T\; s\_k+\backslash frac\; s^T\_k\; s\_k,$ and the Taylor series of the gradient itself (secant equation): :$\backslash nabla\; f(x\_k+s\_k)=\backslash nabla\; f(x\_k)+B\; s\_k,$ is used to update $B$. The DFP formula finds a solution that is symmetric, positive definite and closest to the current approximate value of $B\_k$: :$B\_=$ (I-\gamma_k y_k s_k^T) B_k (I-\gamma_k s_k y_k^T)+\gamma_k y_k y_k^T, where :$y\_k=\backslash nabla\; f(x\_k+s\_k)-\backslash nabla\; f(x\_k),$ :$\backslash gamma\_k\; =\backslash frac.$ and $B\_k$ is a symmetric and positive definite matrix. The corresponding update to the inverse Hessian approximation $H\_k=B\_k^$ is given by: :$H\_=H\_-\backslash frac+\backslash frac.$ $B$ is assumed to be positive definite, and the vectors $s\_k^T$ and $y$ must satisfy the curvature condition: : $s\_k^T\; y\_k=s\_k^T\; B\; s\_k>0.\; \backslash ,$ The DFP formula is quite effective, but it was soon superseded by the BFGS formula, which is its dual (interchanging the roles of y and s). ==See also== * Newton's method * Newton's method in optimization * Quasi-Newton method * Broyden–Fletcher–Goldfarb–Shanno (BFGS) method * L-BFGS method * SR1 formula * Nelder–Mead method 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「Davidon–Fletcher–Powell formula」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.