1. 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. Originally Posted by scorpion007
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

3. Makes perfect sense now, thanks!