Divided differences

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 $(x_{0},y_{0}),\ldots ,(x_{n},y_{n})$ , the method calculates the coefficients of the interpolation polynomial of these points in the Newton form.

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

[Isaacson2014-1] Isaacson, Walter (2014). The Innovators. Simon & Schuster. p. 20. ISBN 978-1-4767-0869-0.

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