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divided differences : ウィキペディア英語版
divided differences

In mathematics, divided differences is a recursive division process.
The method can be used to calculate the coefficients in the interpolation polynomial in the Newton form.
==Definition==

Given ''k+1'' data points
:(x_0, y_0),\ldots,(x_, y_)
The forward divided differences are defined as:
:() := y_\nu, \qquad \nu \in \
:() := \frac,\ldots">, y_ ) - (, y_ )}, \qquad \nu\in\,\ j\in\.
The backward divided differences are defined as:
:() := y_,\qquad \nu \in \
:() := \frac,\ldots" TITLE="y_,\ldots">, y_ )},\ j\in\.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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