1 / 21

Newton’s Divided Difference Polynomial Method of Interpolation

Newton’s Divided Difference Polynomial Method of Interpolation. Newton’s Divided Difference Method. Linear interpolation : Given pass a linear interpolant through the data where. Example.

charo
Download Presentation

Newton’s Divided Difference Polynomial 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. Newton’s Divided Difference Polynomial Method of Interpolation

  2. Newton’s Divided Difference Method Linear interpolation: Given pass a linear interpolant through the data where http://numericalmethods.eng.usf.edu

  3. Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for linear interpolation. Figure 2: Velocity vs. time data for the rocket example Table 1: Velocity as a function of time

  4. Linear Interpolation http://numericalmethods.eng.usf.edu

  5. Linear Interpolation (contd) http://numericalmethods.eng.usf.edu

  6. Quadratic Interpolation http://numericalmethods.eng.usf.edu

  7. Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for quadratic interpolation. Figure 2: Velocity vs. time data for the rocket example Table 1: Velocity as a function of time

  8. Quadratic Interpolation (contd)

  9. Quadratic Interpolation (contd) http://numericalmethods.eng.usf.edu

  10. Quadratic Interpolation (contd)

  11. General Form where Rewriting http://numericalmethods.eng.usf.edu

  12. General Form

  13. General form http://numericalmethods.eng.usf.edu

  14. Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for cubic interpolation. Figure 2: Velocity vs. time data for the rocket example Table 1: Velocity as a function of time

  15. Example The velocity profile is chosen as we need to choose four data points that are closest to http://numericalmethods.eng.usf.edu

  16. Example

  17. Example http://numericalmethods.eng.usf.edu

  18. Comparison Table http://numericalmethods.eng.usf.edu

  19. Latihan Misalkan Nilai-nilai fungsi seperti pada tabel berikut, tentukanlah nilai aproksimasi dari f(0,1), f(0,35), dan f(1,16) berturut-turut menggunakan interpolasi beda terbagi Newton linear, kuadratik, kubik.

  20. Distance from Velocity Profile Find the distance covered by the rocket from t=11s to t=16s ?

  21. Acceleration from Velocity Profile Find the acceleration of the rocket at t=16s given that

More Related