1. Newton’s Divided Difference Polynomial Method of Interpolation
Electrical 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
Thermistors are based on materials’ change in resistance with temperature. A manufacturer of thermistors makes the following observations on a thermistor. Determine the temperature corresponding to ohms using the Newton Divided Difference method for linear interpolation.
R (Ω)
T(°C)
1101.0
911.3
636.0
451.1
25.113
30.131
40.120
50.128

7. Linear Interpolation

8. Linear Interpolation (contd)

9. Quadratic Interpolation

10. Example
Thermistors are based on materials’ change in resistance with temperature. A manufacturer of thermistors makes the following observations on a thermistor. Determine the temperature corresponding to ohms using the Newton Divided Difference method for quadratic interpolation.
R (Ω)
T(°C)
1101.0
911.3
636.0
451.1
25.113
30.131
40.120
50.128

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
Thermistors are based on materials’ change in resistance with temperature. A manufacturer of thermistors makes the following observations on a thermistor. Determine the temperature corresponding to ohms using the Newton Divided Difference method for cubic interpolation.
R (Ω)
T(°C)
1101.0
911.3
636.0
451.1
25.113
30.131
40.120
50.128

18. Example

19. Example

20. Example

21. Comparison Table

22. Actual Calibration R (Ω) T (°C) x(ln R) y(1/T) 1101.0 911.3 636.0
451.1
25.113
30.131
40.120
50.128
7.0040
6.8149
6.4552
6.1117

23. Actual Calibration

24. Actual Calibration

25. Actual Calibration

26. Actual Calibration

27. 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

28. THE END