1. Newton’s Divided Difference Polynomial Method of Interpolation
Computer Engineering Majors
Authors: Autar Kaw, Jai Paul
Transforming Numerical Methods Education for STEM Undergraduates

2. Newton’s Divided Difference Method of Interpolation http://numericalmethods.eng.usf.edu

3. What is Interpolation ?
Given (x0,y0), (x1,y1), …… (xn,yn), find the value of ‘y’ at a value of ‘x’ that is not given.

4. Interpolants Evaluate Differentiate, and Integrate.
Polynomials are the most common choice of interpolants because they are easy to:
Evaluate
Differentiate, and
Integrate.

5. Newton’s Divided Difference Method
Linear interpolation: Given pass a linear interpolant through the data
where

6. Example
A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a rectangular plate. The hole centers in the plate that describe the path the arm needs to take are given below.
If the laser is traversing from x = 2 to x = 4.25 in a linear path, find the value of y at x = 4 using the Newton’s Divided Difference method for linear interpolation.
Figure 2 Location of holes on the rectangular plate.

7. Linear Interpolation

8. Linear Interpolation (contd)

9. Quadratic Interpolation

10. Example
A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a rectangular plate. The hole centers in the plate that describe the path the arm needs to take are given below.
If the laser is traversing from x = 2 to x = 4.25 in a linear path, find the value of y at x = 4 using the Newton’s Divided Difference method for quadratic interpolation.
Figure 2 Location of holes on the rectangular plate.

11. Quadratic Interpolation (contd)

12. Quadratic Interpolation (contd)

13. Quadratic Interpolation (contd)

14. General Form
where
Rewriting

15. General Form

16. General form

17. Example
A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a rectangular plate. The hole centers in the plate that describe the path the arm needs to take are given below.
If the laser is traversing from x = 2 to x = 4.25 in a linear path, find the value of y at x = 4 using the Newton’s Divided Difference method for a fifth order polynomial.
Figure 2 Location of holes on the rectangular plate.

18. Example

19. Example

20. Example

21. Additional Resources
For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit

22. THE END