The Newton Interpolation Polynomial

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Background. Newton Interpolation Polynomial.

 

To construct and evaluate the Newton polynomial of degree [Graphics:np.txtgr1.gif] that passes through the n+1 points [Graphics:np.txtgr2.gif], for [Graphics:np.txtgr3.gif]:

[Graphics:np.txtgr4.gif]

 

Construction for n = 1. [Graphics:np.txtgr5.gif]
Use the two points [Graphics:np.txtgr6.gif].
[Graphics:np.txtgr7.gif]

 

Construction for n = 2. [Graphics:np.txtgr8.gif]
Use the three points [Graphics:np.txtgr9.gif].
[Graphics:np.txtgr10.gif]

The general case us unwieldy and is treated by defining divided differences.

 

 

 

 

(c) John H. Mathews, 1998