1. Lagrangian Interpolation
Chemical Engineering Majors
Authors: Autar Kaw, Jai Paul
Transforming Numerical Methods Education for STEM Undergraduates

2. Lagrange 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. Lagrangian Interpolation

6. Example
To find how much heat is required to bring a kettle of water to boiling point, you are asked to calculate the specific heat of water at 610C. Use a first, second and third order Lagrange polynomial to determine the value of the specific heat at T = 61°C.
Table 1 Specific heat of water as a function of temperature.
Temperature,
Specific heat, 22 42 52 82
100
4181
4179
4186
4199
4217
Figure 2 Specific heat of water vs. temperature.

7. Linear Interpolation

8. Linear Interpolation (contd)

9. Quadratic Interpolation

10. Quadratic Interpolation (contd)

11. Quadratic Interpolation (contd)

12. Cubic Interpolation

13. Cubic Interpolation (contd)

14. Cubic Interpolation (contd)

15. Cubic Interpolation (contd)
The absolute relative approximate error obtained between the results from the second and third order polynomial is

16. Comparison Table

17. 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

18. THE END