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Math Help - newton interpolation problem

  1. #1
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    newton interpolation problem

    with w(x)=(x-x(0))(x-x(1))...(x-x(n)) prove that
    f[x(0),x(1),x(2),..,x(n))]=summation(0,n) (f(x(i))/(derivative(w(x(i))))
    and hence calculate the limit for formula f[x(0),x(1),x(2),..,x(n))] when x(2)->x(1) while all other points remain fixed

    i have done the first part but stuck in the second part of calculating the limit.please help

    note:f[x(0),x(1),x(2),..,x(n))] is the newton forward difference function
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  2. #2
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    Re: newton interpolation problem

    Quote Originally Posted by prasum View Post
    with w(x)=(x-x(0))(x-x(1))...(x-x(n)) prove that
    f[x(0),x(1),x(2),..,x(n))]=summation(0,n) (f(x(i))/(derivative(w(x(i))))
    and hence calculate the limit for formula f[x(0),x(1),x(2),..,x(n))] when x(2)->x(1) while all other points remain fixed

    i have done the first part but stuck in the second part of calculating the limit.please help

    note:f[x(0),x(1),x(2),..,x(n))] is the newton forward difference function
    it sure would be nice if you learned to use LaTex. It's not that hard.

    Is this what you mean?

    $w(x)=\displaystyle \prod_{i=1}^n \left(x-x_i\right)$ prove that

    $f\left(x_0, x_1,\dots, x_n\right)=\displaystyle{\sum_{i=0}^n} \dfrac{f(x_i)}{\dfrac{dw}{dx_i}}$

    and calculate

    $\displaystyle \lim_{x_2 \to x_1}f\left(x_0, x_1,\dots, x_n\right)$
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  3. #3
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    Re: newton interpolation problem

    yes can u please help me with the second part of calculating the limit
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