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Lagrange Method of Interpolation: Understanding Interpolation Techniques

Learn about Lagrangian interpolation, interpolants, and polynomial methods for finding values in numerical analysis. Explore examples like heat calculation and interpolation errors.

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Lagrange Method of Interpolation: Understanding Interpolation Techniques

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  1. Lagrange Method of Interpolation

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

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

  4. Lagrangian Interpolation

  5. 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.

  6. Linear Interpolation

  7. Linear Interpolation (contd)

  8. Quadratic Interpolation

  9. Quadratic Interpolation (contd)

  10. Quadratic Interpolation (contd)

  11. Cubic Interpolation

  12. Cubic Interpolation (contd)

  13. Cubic Interpolation (contd)

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

  15. Comparison Table

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