1. Spline Interpolation Method
Electrical Engineering Majors
Authors: Autar Kaw, Jai Paul
Transforming Numerical Methods Education for STEM Undergraduates

2. Spline 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. Why Splines ?

6. Figure : Higher order polynomial interpolation is a bad idea
Why Splines ?
Figure : Higher order polynomial interpolation is a bad idea

7. Linear Interpolation

8. Linear Interpolation (contd)

9. 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 linear spline interpolation.
R (Ω)
T(°C)
1101.0
911.3
636.0
451.1
25.113
30.131
40.120
50.128

10. Linear Interpolation

11. Quadratic Interpolation

12. Quadratic Interpolation (contd)

13. Quadratic Splines (contd)

14. Quadratic Splines (contd)

15. Quadratic Splines (contd)

16. 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 quadratic spline interpolation.
R (Ω)
T(°C)
1101.0
911.3
636.0
451.1
25.113
30.131
40.120
50.128

17. Solution

18. Solution (contd)

19. Solution (contd)

20. Solution (contd)

21. Solution (contd)

22. Solution (contd)

23. 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

24. THE END