The Newton Interpolation Polynomial

 

 

Definition. Divided Differences.

 

The divided differences for a function f[x] are defined as follows:

[Graphics:np.txtgr12.gif][Graphics:np.txtgr11.gif]

 

The divided difference formulae are used to construct the divided difference table:

[Graphics:np.txtgr12.gif][Graphics:np.txtgr13.gif]

 

The coefficient [Graphics:np.txtgr14.gif] of the Newton polynomial [Graphics:np.txtgr15.gif] is [Graphics:np.txtgr16.gif]
and it is the top element in the column of the k-th divided differences.

 

 

 

 

(c) John H. Mathews, 1998