Quote:
Originally Posted by wgardner
Is there a different way of expressing this derivation without resorting to a vector N of the errors that are being minimized?
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Quote:
Originally Posted by Ether
AO=M;
254 equations in 76 unknowns; (for the example I posted)
system is overdetermined;
there is no exact solution for O;
A'AO=A'M;
76 equations in 76 unknowns;
Exact solution O for this system will be the least squares solution for the original 254x76 system. |
OK, but this doesn't derive that this is the least squares solution: it merely states the result without explaining where it came from. The only derivations I've ever seen start with a formulation like I laid out and find the O that minimizes the squared error term N' N by taking the derivative of N' N with respect to O, setting it equal to zero, and solving for O. Is there another way to show this derivation without N? That was my question, as Oblarg was asking why I bothered to introduce N in the first place.