1 / 15

Lagrange Method of Interpolation

Lagrange Method of Interpolation. What is Interpolation ?. Given (x 0 ,y 0 ), (x 1 ,y 1 ), …… (x n ,y n ), find the value of ‘y’ at a value of ‘x’ that is not given. Interpolants. Polynomials are the most common choice of interpolants because they are easy to: Evaluate Differentiate, and

barbaraeaton
Download Presentation

Lagrange Method of Interpolation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related