Search results
Results from the WOW.Com Content Network
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 ...
The Newton series consists of the terms of the Newton forward difference equation, named after Isaac Newton; in essence, it is the Gregory–Newton interpolation formula [9] (named after Isaac Newton and James Gregory), first published in his Principia Mathematica in 1687, [10] [11] namely the discrete analog of the continuous Taylor expansion,
Since the relationship between divided differences and forward differences is given as: [4] [, +, …, +] =! (), Taking = (), if the representation of x in the previous sections was instead taken to be = +, the Newton forward interpolation formula is expressed as: () = (+) = = () which is the interpolation of all points after .
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.
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.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Given an analytic function (), define the moving difference of f as = ()where is the forward difference operator.Then, provided that f obeys certain summability conditions, then it may be represented in terms of these polynomials as
Billy Donovan hasn’t watched many UConn games. He doesn’t have the time while coaching the NBA’s Chicago Bulls. But he’s seen enough to know the Huskies’ bid to repeat as national champions — they are trying to become the first since Donovan’s Florida team in 2007 to do so — is happening in “a totally different environment.”