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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


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    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


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    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.
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