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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 Numerical continuation ： ウィキペディア英語版 Numerical continuation Numerical continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, :$F(\backslash mathbf\; u,\backslash lambda)\; =\; 0$ The ''parameter'' $\backslash lambda$ is usually a real scalar, and the ''solution'' an ''n''-vector. For a fixed ''parameter value'' $\backslash lambda$, $F(\backslash ast,\backslash lambda)$ maps Euclidean n-space into itself. Often the original mapping $F$ is from a Banach space into itself, and the Euclidean n-space is a finite-dimensional approximation to the Banach space. A steady state, or fixed point, of a parameterized family of flows or maps are of this form, and by discretizing trajectories of a flow or iterating a map, periodic orbits and heteroclinic orbits can also be posed as a solution of $F=0$. == Other forms == In some nonlinear systems, parameters are explicit. In others they are implicit, and the system of nonlinear equations is written :$F(\backslash mathbf\; u)\; =\; 0$ where $\backslash mathbf\; u$ is an ''n''-vector, and its image $F(\backslash mathbf\; u)$ is an ''n-1'' vector. This formulation, without an explicit parameter space is not usually suitable for the formulations in the following sections, because they refer to parameterized autonomous nonlinear dynamical systems of the form: :$\backslash mathbf\; u\text{'}\; =\; F(\backslash mathbf\; u,\backslash lambda)$ However, in an algebraic system there is no distinction between unknowns $\backslash mathbf\; u$ and the parameters. 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「Numerical continuation」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.