Example 2.  Error Analysis.  Investigate the error for the Newton polynomial approximations in Example 1.

Solution 2 (a).

Investigate the error over the interval    for the Newton interpolation polynomial  ,  of degree n = 1.

Use formula(i).       is valid for  ,  and find the error bound for this example.

Thus,    is valid for  ,  which is a little bit larger than the maximum error  0.00497089.  After all, it is an error bound.  

(c) John H. Mathews 2004