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Divided differences information


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 a sequence of data points , the method calculates the coefficients of the interpolation polynomial of these points in the Newton form.

  1. ^ Isaacson, Walter (2014). The Innovators. Simon & Schuster. p. 20. ISBN 978-1-4767-0869-0.

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Divided differences

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first created by Charles Babbage. The name difference engine is derived from the method of divided differences, a way to interpolate or tabulate functions...

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Newton's divided differences interpolation polynomial because the coefficients of the polynomial are calculated using Newton's divided differences method...

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\ldots ,y_{i}].\end{aligned}}} Since relationship between divided differences and forward differences is given as: [ y j , y j + 1 , … , y j + n ] = 1 n !...

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interpolation method, in that both can be derived from the calculation of divided differences. However, there are other methods for computing a Hermite interpolating...

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x ] {\displaystyle f[x_{0},\ldots ,x_{k},x]} is the notation for divided differences. Alternatively, the remainder can be expressed as a contour integral...

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its differences, it tends to give more weight to larger differences and less weight to smaller differences compared to the mean absolute difference. When...

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transcription delimiters. Differences in pronunciation between American English (AmE) and British English (BrE) can be divided into differences in accent (i.e....

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constants Different forms for the interpolant: Newton polynomial Divided differences Neville's algorithm — for evaluating the interpolant; based on the...

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Identric mean

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generalized to more variables according by the mean value theorem for divided differences. The identric mean is a special case of the Stolarsky mean. Mean...

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