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In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. [citation needed] Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation. [1] Divided differences is a recursive division process.
Given n + 1 points, there is a unique polynomial of degree ≤ n which goes through the given points. Neville's algorithm evaluates this polynomial. Neville's algorithm evaluates this polynomial. Neville's algorithm is based on the Newton form of the interpolating polynomial and the recursion relation for the divided differences .
The simplest method is to use finite difference approximations. A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). [1] Choosing a small number h, h represents a small change in x, and it can be either positive or negative.
That is, in Benders decomposition, the variables of the original problem are divided into two subsets so that a first-stage master problem is solved over the first set of variables, and the values for the second set of variables are determined in a second-stage subproblem for a given first-stage solution.
Download QR code; Print/export Download as PDF; Printable version; ... where the nth derivative of f equals n ! times the nth divided difference at these points: ...
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