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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 Spline interpolation ： ウィキペディア英語版 Spline interpolation In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. Spline interpolation is often preferred over polynomial interpolation because the interpolation error can be made small even when using low degree polynomials for the spline. Spline interpolation avoids the problem of Runge's phenomenon, in which oscillation can occur between points when interpolating using high degree polynomials. ==Introduction== Originally, ''spline'' was a term for elastic rulers that were bent to pass through a number of predefined points ("knots"). These were used to make technical drawings for shipbuilding and construction by hand, as illustrated by Figure 1. The approach to mathematically model the shape of such elastic rulers fixed by knots $\backslash left\; \backslash$ is to interpolate between all the pairs of knots $(x\_,\; y\_)$ and $(x\_i,\; y\_i)$ with polynomials $y=q\_i(x),\; i=1,2,\backslash cdots,n$. The curvature of a curve $y=f(x)$ is given by: :$\backslash kappa=\; \backslash frac\; q\text{'}\_i(x\_i)\; =\; q\text{'}\_(x\_i)\; \backslash \backslash \; q\text{'}\text{'}\_i(x\_i)\; =\; q\text{'}\text{'}\_(x\_i)\; \backslash end\; \backslash qquad\; 1\; \backslash le\; i\; \backslash le\; n-1$ This can only be achieved if polynomials of degree 3 or higher are used. The classical approach is to use polynomials of degree 3 — the case of cubic splines. 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「Spline interpolation」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.