Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS
 Lagrange interpolation formula (Theorem)

Let be points in the plane ( for ). Then there exists a unique polynomial of degree at most such that for .

Such polynomial can be found using Lagrange's interpolation formula:

where .

To see this, notice that the above formula is the same as

and that for all , every numerator except one vanishes, and this numerator will be identical to the denominator, making the overall quotient equal to 1. Therefore, each equals .

"Lagrange interpolation formula" is owned by drini. [ full author list (3) | owner history (1) ]
(view preamble)

 View style: HTML with imagespage imagesTeX source

 Other names: Lagrange's Interpolation formula
 Keywords: Interpolation, Extrapolation, Polynomial, Derivative

 Attachments: proof of uniqueness of Lagrange Interpolation formula (Proof) by mps

Cross-references: quotient, denominator, vanishes, numerator, formula, degree, polynomial, plane, points
There are 6 references to this entry.

This is version 10 of Lagrange interpolation formula, born on 2001-10-15, modified 2005-02-03.
Object id is 229, canonical name is LagrangeInterpolationFormula.
Accessed 23301 times total.

Classification:
 AMS MSC: 41A05 (Approximations and expansions :: Interpolation) 65D05 (Numerical analysis :: Numerical approximation and computational geometry :: Interpolation)