翻訳と辞書 Words near each other ・ Symmetric hypergraph theorem ・ Symmetric in Design ・ Symmetric inverse semigroup ・ Symmetric level-index arithmetic ・ Symmetric matrix ・ Symmetric mean absolute percentage error ・ Symmetric monoidal category ・ Symmetric multiprocessing ・ Symmetric multiprocessor system ・ Symmetric obstruction theory ・ Symmetric Phase Recording ・ Symmetric polynomial ・ Symmetric probability distribution ・ Symmetric product ・ Symmetric product of an algebraic curve ・ Symmetric rank-one ・ Symmetric relation ・ Symmetric scale ・ Symmetric set ・ Symmetric space ・ Symmetric space (disambiguation) ・ Symmetric spectrum ・ Symmetric successive overrelaxation ・ Symmetric tensor ・ Symmetric Turing machine ・ Symmetric variety ・ Symmetric-key algorithm ・ Symmetrical All Wheel Drive ・ Symmetrical components ・ Symmetrical Defense 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 Symmetric rank-one ： ウィキペディア英語版 Symmetric rank-one The Symmetric Rank 1 (SR1) method is a quasi-Newton method to update the second derivative (Hessian) based on the derivatives (gradients) calculated at two points. It is a generalization to the secant method for a multidimensional problem. This update maintains the ''symmetry'' of the matrix but does ''not'' guarantee that the update be ''positive definite''. The sequence of Hessian approximations generated by the SR1 method converges to the true Hessian under mild conditions, in theory; in practice, the approximate Hessians generated by the SR1 method show faster progress towards the true Hessian than do popular alternatives (BFGS or DFP), in preliminary numerical experiments. The SR1 method has computational advantages for sparse or partially separable problems. A twice continuously differentiable function $x\; \backslash mapsto\; f(x)$ has a gradient ($\backslash nabla\; f$) and Hessian matrix $B$: The function $f$ has an expansion as a Taylor series at $x\_0$, which can be truncated ::$f(x\_0+\backslash Delta\; x)=f(x\_0)+\backslash nabla\; f(x\_0)^T\; \backslash Delta\; x+\backslash frac\; \backslash Delta\; x^T\; \backslash Delta\; x$; its gradient has a Taylor-series approximation also ::$\backslash nabla\; f(x\_0+\backslash Delta\; x)=\backslash nabla\; f(x\_0)+B\; \backslash Delta\; x$, which is used to update $B$. The above secant-equation need not have a unique solution $B$. The SR1 formula computes (via an update of rank 1) the symmetric solution that is closest to the current approximate-value $B\_k$: ::$B\_=B\_+\backslash frac$, where ::$y\_k=\backslash nabla\; f(x\_k+\backslash Delta\; x\_k)-\backslash nabla\; f(x\_k)$. The corresponding update to the approximate inverse-Hessian $H\_k=B\_k^$ is ::$H\_=H\_+\backslash frac$. The SR1 formula has been rediscovered a number of times. A drawback is that the denominator can vanish. Some authors have suggested that the update be applied only if ::$|\backslash Delta\; x\_k^T\; (y\_k-B\_k\; \backslash Delta\; x\_k)|\backslash geq\; r\; \backslash |\backslash Delta\; x\_k\backslash |\backslash cdot\; \backslash |y\_k-B\_k\; \backslash Delta\; x\_k\backslash |$, where $r\backslash in(0,1)$ is a small number, e.g. $10^$. ==See also== * Quasi-Newton method * Newton's method in optimization * Broyden-Fletcher-Goldfarb-Shanno (BFGS) method * L-BFGS 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「Symmetric rank-one」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.