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  2. 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 ...

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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 =.

  8. Testing forgotten rape kits could free the innocent. Here’s ...

    www.aol.com/testing-forgotten-rape-kits-could...

    In 2000, New York City began testing old rape kits with updated methods and comparing the results with profiles in the state DNA database. Three years later, the evidence in Mercer’s case ...

  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.