Least Square Minimisation and Partial Differentiation

[skaboy607]

Homework Statement

I am trying to understand how some equations are obtained in some lecture notes I have.

This is my starting equation-http://i423.photobucket.com/albums/pp315/skaboy607/StartEquation.png

And I need to satisfy these conditions

http://i423.photobucket.com/albums/pp315/skaboy607/Conditions.png

And somehow get to here

http://i423.photobucket.com/albums/pp315/skaboy607/WhatIshouldendupwith.png

Homework Equations

all above

The Attempt at a Solution

I've stared at it for a while now and just don't get it. Wouldn't the square come down in front of the brackets? and surely the other constants would dissapear?

any help most appreciated..

Thanks

 

[Billy Bob]

Looking at only one term of the summation, if F=[R1*a - R2*b + R3 - c]^2 (here a, b, and c are constants), then partial of F with respect to R1 is, by the chain rule,

2[R1*a - R2*b + R3 - c]^1 * a,

where a is the derivative of R1*a - R2*b + R3 - c with respect to R1.

But your 2 "disappears" when you set this equal to 0 and divide by 2.

"a" would disappear too, if there were no summation, but in this case "a" is really a_i, so it can't be brought outside of the summation over i.

 

[skaboy607]

Nice one, thanks very much.

 

[skaboy607]

Hi, I've done this now. But I have just a quick question about it? The way I did it was to multiply the brackets then do partial differentiation with respect to R1, then divide 2 and take out cos(theta) as a common factor. This was quite time consuming, is there something i don't know about that will enable me to look at an equation like that, and jump to final stage like you did so I can miss out the bits in the middle?

Thanks