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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.

  3. Newton polynomial - Wikipedia

    en.wikipedia.org/wiki/Newton_polynomial

    The divided difference methods have the advantage that more data points can be added, for improved accuracy. The terms based on the previous data points can continue to be used. With the ordinary Lagrange formula, to do the problem with more data points would require re-doing the whole problem.

  4. 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 =.

  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. 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

  7. Should kids in a family get the same amount of holiday gifts ...

    www.aol.com/news/kids-family-same-amount-holiday...

    Hoda Kotb’s daughters Haley and Hope will unbox an equal amount of presents on Christmas morning while Jenna Bush Hager's kids get different amounts.

  8. What is the 5th house in astrology? An astrologer breaks it down

    www.aol.com/5th-house-astrology-astrologer...

    All astrological charts, from natal charts to event charts, are divided up into 12 sections, also known as houses. Each house falls into a different sign, starting with the first house and ...

  9. Finite difference - Wikipedia

    en.wikipedia.org/wiki/Finite_difference

    A finite difference is a mathematical expression of the form f (x + b) − f (x + a).If a finite difference is divided by b − a, one gets a difference quotient.The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.