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  2. 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 ...

  3. 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.

  4. 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.

  5. 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.

  6. Hermite interpolation - Wikipedia

    en.wikipedia.org/wiki/Hermite_interpolation

    In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation. Lagrange interpolation allows computing a polynomial of degree less than n that takes the same value at n given points as a given function.

  7. Difference polynomials - Wikipedia

    en.wikipedia.org/wiki/Difference_polynomials

    In mathematics, in the area of complex analysis, the general difference polynomials are a polynomial sequence, a certain subclass of the Sheffer polynomials, which include the Newton polynomials, Selberg's polynomials, and the Stirling interpolation polynomials as special cases.

  8. Mean value theorem (divided differences) - Wikipedia

    en.wikipedia.org/wiki/Mean_value_theorem...

    Let be the Lagrange interpolation polynomial for f at x 0, ..., x n.Then it follows from the Newton form of that the highest order term of is [, …,].. Let be the remainder of the interpolation, defined by =.

  9. Talk:Newton polynomial - Wikipedia

    en.wikipedia.org/wiki/Talk:Newton_polynomial

    A frequent use of polynomial interpolation is to determine whether or not linear interpolation will be accurate enough. ...by evaluating the quadratic term of a divided-difference method (to find out if it's big enough to matter in the problem). Of course only a divided-difference method can be used for that determination.