ABSTRACT
Substituting these values into Eqs. and (5.11 b) yields the solution for the divided difference polynomial:
P;(3.5) = -0.084040 + [2(3.5) - (3.4 + 3.5)](0.023400) = -0.081700 P;(3.5) = 2(0.023400) = 0.046800
(5.14a) (5.14b)
The results obtained by the three procedures are identical since the same three points are used in all three procedures. The error in f'(3.5) is Error = f'(3.5) - P;(3.5) = -0.081700 - (-0.081633) = -0.000067, and the error in 1"(3.5) is Error =1"(3.5)- P~(3.5)= 0.046800 - (0.046647) = 0.000153.
