Least squares

From: John Dee (johndee_at_hotmail.com)
Date: 02/27/05 

Date: Sun, 27 Feb 2005 17:52:03 +0100

To solve a least squares problem, one minimizes
sum i=0:N | f(x_i)-P(x_i,theta) |^2
in terms of the unknown parameters theta of a polynomial P, for all values of x.
r=f(x_i)-P(x_i,theta) , represents the residual.

When r is complex, this means that the magnitude of the residue is
squared, but i don't understand why this must be squared, since the
magnitude is always positive. When dropping the square, I think one is
solving a different problem. Can someone point this out for me?

Thanks
John

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