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Math Help - Least Squares Approx

  1. #1
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    Least Squares Approx

    Hi, could someone just start me off here?

    I think it has something to do with \partial E / \partial a_j, j = 0, 1, 2, ..., n. But not sure exactly what to do.

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  2. #2
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    Quote Originally Posted by scorpion007 View Post
    Hi, could someone just start me off here?

    I think it has something to do with \partial E / \partial a_j, j = 0, 1, 2, ..., n. But not sure exactly what to do.

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    You want the mininum of:

    E=\sum_{i=0}^m w_i (f_i-\phi (x;a_0, .. , a_n))^2

    at the minimum:

    \frac{\partial E}{\partial a_j}=0

    or:

    \sum_{i=0}^m 2 x^j w_i(f_i-\phi(x;a_0, .. , a_n))=0

    rearranging:

    \sum_{i=0}^m x^j w_i\phi(x;a_0, .. , a_n))=\sum_{i=0}^m x^j w_i f_i

    Now rearrange the left hand side.

    CB
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  3. #3
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    Makes perfect sense now, thanks!
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