• Support PF! Buy your school textbooks, materials and every day products Here!

Least Square Minimisation and Partial Differentiation

  • Thread starter skaboy607
  • Start date
  • #1
108
0

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 [Broken]

And I need to satisfy these conditions

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

And somehow get to here

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

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
 
Last edited by a moderator:

Answers and Replies

  • #2
392
0
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.
 
  • #3
108
0
Nice one, thanks very much.
 
  • #4
108
0
Hi, ive 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
 

Related Threads for: Least Square Minimisation and Partial Differentiation

Replies
6
Views
466
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
7
Views
672
  • Last Post
Replies
3
Views
928
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
757
  • Last Post
Replies
4
Views
864
Top