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  2. Divided differences - Wikipedia

    en.wikipedia.org/wiki/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.

  3. Newton polynomial - Wikipedia

    en.wikipedia.org/wiki/Newton_polynomial

    Taking = for some unknown function in Newton divided difference formulas, if the representation of x in the previous sections was instead taken to be = +, in terms of forward differences, the Newton forward interpolation formula is expressed as: () = (+) = = () whereas for the same in terms of backward differences, the Newton backward ...

  4. Difference engine - Wikipedia

    en.wikipedia.org/wiki/Difference_engine

    The principle of a difference engine is Newton's method of divided differences. If the initial value of a polynomial (and of its finite differences) is calculated by some means for some value of X, the difference engine can calculate any number of nearby values, using the method generally known as the method of finite differences.

  5. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    This expression is Newton's difference quotient (also known as a first-order divided difference). The slope of this secant line differs from the slope of the tangent line by an amount that is approximately proportional to h. As h approaches zero, the slope of the secant line approaches the slope of the tangent line.

  6. Neville's algorithm - Wikipedia

    en.wikipedia.org/wiki/Neville's_algorithm

    In mathematics, Neville's algorithm is an algorithm used for polynomial interpolation that was derived by the mathematician Eric Harold Neville in 1934. Given n + 1 points, there is a unique polynomial of degree ≤ n which goes through the given points.

  7. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    One method is to write the interpolation polynomial in the Newton form (i.e. using Newton basis) and use the method of divided differences to construct the coefficients, e.g. Neville's algorithm. The cost is O(n 2) operations.

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  9. Hermite interpolation - Wikipedia

    en.wikipedia.org/wiki/Hermite_interpolation

    Hermite's method of interpolation is closely related to the Newton's interpolation method, in that both can be derived from the calculation of divided differences. However, there are other methods for computing a Hermite interpolating polynomial.