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Math Help - find polynomial

  1. #1
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    find polynomial

    Hi,

    I'm not sure whether this is a suitable problem for this section. Anyway, I have a set of points and I need to find a polynomial.

    The points are..
    (0,3),(1,10),(2,10),(3,10)....(50,10)

    how do I get the polynomial?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: find polynomial

    Quote Originally Posted by mccvinodh View Post
    Hi,

    I'm not sure whether this is a suitable problem for this section. Anyway, I have a set of points and I need to find a polynomial.

    The points are..
    (0,3),(1,10),(2,10),(3,10)....(50,10)

    how do I get the polynomial?
    The best-fit would be the line y = 10.
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  3. #3
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    Re: find polynomial

    yeah.. but I need to find the value at x = -1. In that y = 10 is not the perfect fir.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: find polynomial

    Quote Originally Posted by mccvinodh View Post
    The points are.. (0,3),(1,10),(2,10),(3,10)....(50,10) how do I get the polynomial?
    If you mean the polynomial passing through those points, look here:

    Lagrange polynomial
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  5. #5
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    Re: find polynomial

    Quote Originally Posted by FernandoRevilla View Post
    If you mean the polynomial passing through those points, look here:

    Lagrange polynomial

    Yes. I need the one through the points. But the resulting polynomial will be of degree 50. Am I right? Is that the simplest that I can get?

    Thank you for your suggestion!
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Re: find polynomial

    You can express p(x)=3L_0(x)+10\sum_{i=1}^{50}L_i(x) where L_i(x)=\prod_{j\neq i}\frac{x-j}{i-j}\;(i=0,1,2,\ldots,50)
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