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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 Affine arithmetic ： ウィキペディア英語版 Affine arithmetic Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine forms) of certain primitive variables, which stand for sources of uncertainty in the data or approximations made during the computation. Affine arithmetic is meant to be an improvement on interval arithmetic (IA), and is similar to generalized interval arithmetic, first-order Taylor arithmetic, the center-slope model, and ellipsoid calculus — in the sense that it is an automatic method to derive first-order guaranteed approximations to general formulas. Affine arithmetic is potentially useful in every numeric problem where one needs guaranteed enclosures to smooth functions, such as solving systems of non-linear equations, analyzing dynamical systems, integrating functions differential equations, etc. Applications include ray tracing, plotting curves, intersecting implicit and parametric surfaces, error analysis (mathematics), process control, worst-case analysis of electric circuits, and more. ==Definition== In affine arithmetic, each input or computed quantity ''x'' is represented by a formula $x\; =\; x\_0\; +\; x\_1\; \backslash epsilon\_1\; +\; x\_2\; \backslash epsilon\_2\; +\; \{\}$$\backslash cdots$$\{\}\; +\; x\_n\; \backslash epsilon\_n$ where $x\_0,\; x\_1,\; x\_2,$$\backslash dots,$$x\_n$ are known floating-point numbers, and $\backslash epsilon\_1,\; \backslash epsilon\_2,\backslash epsilon\_n$ are symbolic variables whose values are only known to lie in the range (). Thus, for example, a quantity ''X'' which is known to lie in the range () can be represented by the affine form $x\; =\; 5\; +\; 2\; \backslash epsilon\_k$, for some ''k''. Conversely, the form $x\; =\; 10\; +\; 2\; \backslash epsilon\_3\; -\; 5\; \backslash epsilon\_8$ implies that the corresponding quantity ''X'' lies in the range (). The sharing of a symbol $\backslash epsilon\_j$ among two affine forms $x$, $y$ implies that the corresponding quantities ''X'', ''Y'' are partially dependent, in the sense that their joint range is smaller than the Cartesian product of their separate ranges. For example, if $x\; =\; 10\; +\; 2\; \backslash epsilon\_3\; -\; 6\; \backslash epsilon\_8$ and $y\; =\; 20\; +\; 3\; \backslash epsilon\_4\; +\; 4\; \backslash epsilon\_8$, then the individual ranges of ''X'' and ''Y'' are () and (), but the joint range of the pair (''X'',''Y'') is the hexagon with corners (2,27), (6,27), (18,19), (18,13), (14,13), (2,21) — which is a proper subset of the rectangle ()×(). 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「Affine arithmetic」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.