Newton's Polynomial Interpolation

 

For image002ag interpolation points image004ag, image006ag, the Newton interpolating polynomial image008ag is given by:

 

image010ag

 

The interpolation conditions, image012ag, image006ag, give rise to a system of image002ag linear equations for the image002ag coefficients image014ag.

 

Divided differences of first and higher order are defined by:

 

image016ag,

 

which remain unchanged under permutations of the different nodes and allow us to obtain the interpolating coefficients, image014ag, as:

 

image018ag

 

note Because of the Existence and Uniqueness Theorem, the polynomials produced by Newton's and Lagrange's methods are the same, except for the method by which they are inferred.

 

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