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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 Convex combination ： ウィキペディア英語版 Convex combination In convex geometry, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1. More formally, given a finite number of points $x\_1,\; x\_2,\; \backslash dots,\; x\_n\backslash ,$ in a real vector space, a convex combination of these points is a point of the form :$\backslash alpha\_1x\_1+\backslash alpha\_2x\_2+\backslash cdots+\backslash alpha\_nx\_n$ where the real numbers $\backslash alpha\_i\backslash ,$ satisfy $\backslash alpha\_i\backslash ge\; 0$ and $\backslash alpha\_1+\backslash alpha\_2+\backslash cdots+\backslash alpha\_n=1.$ As a particular example, every convex combination of two points lies on the line segment between the points. The convex hull of the given points is identical to the set of all their convex combinations. There exist subsets of a vector space that are not closed under linear combinations but are closed under convex combinations. For example, the interval $()$ is convex but generates the real-number line under linear combinations. Another example is the convex set of probability distributions, as linear combinations preserve neither nonnegativity nor affinity (i.e., having total integral one). ==Other objects== *Similarly, a convex combination $X$ of probability distributions $Y\_i$ is a weighted sum (where $\backslash alpha\_i$ satisfy the same constraints as above) of its component probability distributions, often called a finite mixture distribution, with probability density function: :$f\_(x)\; =\; \backslash sum\_^\; \backslash alpha\_i\; f\_(x)$ 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「Convex combination」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.