Problem 17.5.
Given the data
Calculate f(4) using Newton's interpolating polynomials of order 1 through 4. Choose your base points to attain good accuracy. That is, the points should be centered around and as close as possible to the unknown. What do your results indicate regarding the order of the polynomial used to generate the data in the table?
Solution:
The points can be ordered so that they are close to and centered around the unknown. A divided-difference table can then be developed as:
Note that the fact that the fourth divided difference is zero means that the data was generated with a third-order polynomial.
No comments:
Post a Comment