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Math Help - Interpolation #2

  1. #1
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    Interpolation #2

    Im working on higher degree interpolation:

    I'm asked to explain why

    L0(x) + L1(x) + L2(x) + L3(x) = 1 for n=3

    Not sure why this is...any advice? Thanks.
    Last edited by mr fantastic; October 17th 2009 at 10:10 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Im working on higher degree interpolation:

    I'm asked to explain why

    L0(x) + L1(x) + L2(x) + L3(x) = 1 for n=3

    Not sure why this is...any advice? Thanks.
    I have no idea what you are doing. What Data are you interpolating? Is this a third degree interpolation? What are L0, L1, L2, and L3?

    Just offhand it looks to me like this is saying that you are giving "equal weight" to the four calculations but other than that I can't say without more information.
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  3. #3
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    Ok...sorry.

    The hint given is to use Pn(x) = y0L0(x) + y1L1(x) + ... + ynLn(x).

    (This is the interpolating polynomial of degree >= n)

    So, Im supposed to use the above hint with suitable choices for {y0, y1, y2, y3) to show:

    L0(x) + L1(x) + L2(x) + L3(x) = 1. Any advice...
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  4. #4
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    Quote Originally Posted by jzellt View Post
    Ok...sorry.

    The hint given is to use Pn(x) = y0L0(x) + y1L1(x) + ... + ynLn(x).

    (This is the interpolating polynomial of degree >= n)

    So, Im supposed to use the above hint with suitable choices for {y0, y1, y2, y3) to show:

    L0(x) + L1(x) + L2(x) + L3(x) = 1. Any advice...
    This still makes no sense.
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