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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

    Newton's form has the simplicity that the new points are always added at one end: Newton's forward formula can add new points to the right, and Newton's backward formula can add new points to the left. The accuracy of polynomial interpolation depends on how close the interpolated point is to the middle of the x values of the set of points used ...

  4. Difference engine - Wikipedia

    en.wikipedia.org/wiki/Difference_engine

    A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was first created by Charles Babbage . The name difference engine is derived from the method of divided differences , a way to interpolate or tabulate functions by using a small set of polynomial co-efficients.

  5. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    In fact, all the finite-difference formulae are ill-conditioned [4] and due to cancellation will produce a value of zero if h is small enough. [5] If too large, the calculation of the slope of the secant line will be more accurately calculated, but the estimate of the slope of the tangent by using the secant could be worse. [6]

  6. Neville's algorithm - Wikipedia

    en.wikipedia.org/wiki/Neville's_algorithm

    This process yields p 0,4 (x), the value of the polynomial going through the n + 1 data points (x i, y i) at the point x. This algorithm needs O(n 2) floating point operations to interpolate a single point, and O(n 3) floating point operations to interpolate a polynomial of degree n.

  7. Notation for differentiation - Wikipedia

    en.wikipedia.org/wiki/Notation_for_differentiation

    Isaac Newton's notation for differentiation (also called the dot notation, fluxions, or sometimes, crudely, the flyspeck notation [11] for differentiation) places a dot over the dependent variable. That is, if y is a function of t , then the derivative of y with respect to t is

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  9. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.Starting with a few accurately computed data points, the corresponding interpolation polynomial will approximate the function at an arbitrary nearby point.