Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Numerical analysis question.

  1. Nov 1, 2006 #1
    in newton forward differece method.
    how can i know that i reached the best interpolation????

    for example in a function like sqrt(x) for Xi=1,1.05,1.10,1.15,1.20,1.25,1.3

    the best interpolation is at P3(x) why???how can i know???
    this really makes me conused:confused: :confused:

    if anyone helped me i will be grateful
     
  2. jcsd
  3. Nov 29, 2006 #2
    in newton forward differece method.

    Asalam o Alikum

    Mr ,
    Value of f(x) at that point define you where the best interpolation between the point is exsist
     
  4. Dec 26, 2006 #3
    simply you construct the table and you will find for this example that after certain iteration the numbers in a certain column will be the same or of accuracy better than that required by the question. this is when you stop . .
     
  5. Dec 26, 2006 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What do you mean by "best"? There exist an infinite number of, say, cubic polynomials that interpolate the points you give. One possible definition of "best" is that [itex]\Sigma |f(x_i)- y_i|[/itex] be a minimum. Another is [itex]Max |f(x_i)- y_i|[/itex] be a minimum and yet another is that [itex]\sqrt{\int (f(x_i)- y_i)^2 dx}[/itex] be a minimum. Each of those has applications.
     
  6. Dec 29, 2006 #5

    ssd

    User Avatar

    Very true sir, I was just going to mention the same.
     
  7. Feb 21, 2007 #6
    :) it is too late, sir i got my answer once i posted the question.(it is too late all)

    any way thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Numerical analysis question.
  1. Analysis Question (Replies: 2)

  2. Numerical Analysis (Replies: 7)

  3. A question in analysis (Replies: 5)

  4. Numerical Analysis (Replies: 2)

Loading...