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Math Help - Series elimination

  1. #1
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    Series elimination

    In doing least squares, I end up with a system of linear equations consisting of series that I have no idea how to eliminate. The system of linear equations consists of the following:

    C*n + D*∑ Ai = ∑ Bi
    C*∑ Ai + D*∑ (Ai)^2 = ∑ AiBi

    I need to solve for C and D. All series are from i = 1:n. My calculus is rusty so I don't quite recall how I can eliminate any of the series. Any help would be appreciated, thanks.
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  2. #2
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    Quote Originally Posted by algorith View Post
    In doing least squares, I end up with a system of linear equations consisting of series that I have no idea how to eliminate. The system of linear equations consists of the following:

    C*n + D*∑ Ai = ∑ Bi
    C*∑ Ai + D*∑ (Ai)^2 = ∑ AiBi

    I need to solve for C and D. All series are from i = 1:n. My calculus is rusty so I don't quite recall how I can eliminate any of the series. Any help would be appreciated, thanks.
    Cn + D\sum{Ai} = \sum{Bi}
    C\sum{Ai} + D\sum{(Ai)^2} = \sum{AiBi}.

    Multiply equation 1 by \sum{Ai} and multiply equation 2 by n.

    Then you get

    Cn\sum{Ai} + D\left[\sum{Ai}\right]^2 = \sum{Ai}\sum{Bi}
    Cn\sum{Ai} + Dn\sum{(Ai)^2} = n\sum{AiBi}.


    Now you should be able to eliminate the C terms.
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  3. #3
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    Awesome, thanks a bunch.
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