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单词 Divided differences
释义

Divided differences

原声例句
还乡

A clear line of difference divided like a tangible fence her experience within this maze of motion from her experience without it.

她在参加舞蹈前的感受与置身于这种婆娑多姿的舞蹈中的感受是截然不同的,就像其间有一道有形的栅栏,将它们清晰地区分开来。

中文百科

均差

《自然哲学的数学原理》的第三编“宇宙体系”的引理五的图例。这里在横坐标上有6个点H,I,K,L,M,N,对应着6个值A,B,C,D,E,F,生成一个多项式函数对这6个点上有对应的6个值,计算任意点S对应的值R。牛顿给出了间距为单位值和任意值的两种情况。

均差(Divided differences)是递归除法过程。在数值分析中,也称差商Difference quotient),可用于计算牛顿多项式形式的多项式插值的系数。

给定n+1个数据点

(x_0, y_0),\ldots,(x_{n}, y_{n})

定义前向均差为:

\begin{align}
 \mathopen[y_\nu] &= y_\nu, \quad \nu \in \{ 0,\ldots,n\} \\
 \mathopen[y_\nu,\ldots,y_{\nu+j}] &= \frac{[y_{\nu+1},\ldots , y_{\nu+j}] - [y_{\nu},\ldots , y_{\nu+j-1}]}{x_{\nu+jx_\nu}, \quad \nu\in\{0,\ldots,n-j\},\ j\in\{1,\ldots,n\}. \\
\end{align}

定义后向均差为:

\begin{align}
 \mathopen[y_\nu] &= y_{\nu},\quad \nu \in \{ 0,\ldots,n\} \\
 \mathopen[y_\nu,\ldots,y_{\nu-j}] &= \frac{[y_\nu,\ldots , y_{\nu-j+1}] - [y_{\nu-1},\ldots , y_{\nu-j}]}{x_\nu - x_{\nu-j}}, \quad \nu\in\{j,\ldots,n\},\ j\in\{1,\ldots,n\}. \\
\end{align}
英语百科

Divided differences 均差

In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. Charles Babbage's Difference engine, an early mechanical calculator, was designed to use this algorithm in its operation.

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更新时间:2025/6/21 1:08:42