# divided differences

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## divided differences

[də′vīd·əd ′dif·rən·səs]
(mathematics)
Quantities which are used in the interpolation or numerical calculation or integration of a function when the function is known at a series of points which are not equally spaced, and which are formed by various operations on the difference between the values of the function at successive points.
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where an empty product of divided differences stands for the function evaluated in [x.
n] corresponds a divided difference [[partial derivative].
n] separately, can be symmetrized using the divided difference
n}] [subset] R, n [greater than or equal to] 1, divided differences are recursively defined as follows.
The same ideas give rise to the definition of complex divided differences.
We define the complex divided differences for the knot sequence [N.
Among those are the endpoint interpolation property, the shape-preserving properties in the case 0 < q < 1, and the representation via divided differences.
44]) the divided differences of f can be expressed as
This question was first considered by Ullrich , who introduced the exponential divided differences (EDD) for the case when [[LAMBDA].
exponential' divided differences EDD corresponding to [[mu].
In this case, the method is reduced to computing various orders of Newton divided differences and is therefore robust, efficient, and easy to implement.
3) can be expressed using Newton divided differences as

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