1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Least Squares Approximation

  1. Sep 8, 2015 #1
    • Member warned about not using the HW template


    My apologies for having to post in an image, my latex skills are not good enough for the question at hand :(

    a) There is no solution since the system has more unknowns than equations (the equations are equal giving 1=2 which does not make sense).

    b) I get a solution of \begin{bmatrix}1 \\1 \\ 3/2 \end{bmatrix}
    for u.

    c) I am not sure how to prove this directly, since there are no values for x,y or z.
     
  2. jcsd
  3. Sep 8, 2015 #2

    RUber

    User Avatar
    Homework Helper

    First off, I do not see the picture for the problem, just the solution. Second, you should use the homework template in this forum.
     
  4. Sep 8, 2015 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper


    If the problem is not very complicated to state, just type it out in plain text. LaTeX is great, but don't let not knowing it stand in your way.
     
  5. Sep 9, 2015 #4
    Again, my apologies. It seems that I accidentally deleted the image.
    So these are the questions
    O6gHNRY.jpg
    I did (a) and (b) as mentioned above and there are no relevant formulae or theorems that I am aware of for part (c).
     
  6. Sep 9, 2015 #5

    RUber

    User Avatar
    Homework Helper

    Right. For part b, anything that lands you at x - y + z = 3/2 is correct.
    For part c, you are asked to show that any other choice for x, y, z such that x-y+z is not equal to 3/2, (x-y+z - 1)^2 + (x-y+z-2)^2 > (3/2 - 1)^2 + (3/2-2)^2 and equal only when x-y+z = 3/2.
    There are plenty of methods to attack the problem, but you should be able to make a good argument without referring to formulae or theorems.
     
  7. Sep 9, 2015 #6

    WWGD

    User Avatar
    Science Advisor
    Gold Member

    For (c), Least Squares is supposed to minimize the norm as defined. I think it minimizes the L^2 -norm. Still, you have a reference there for SG section 12.6. Did you check it out?
     
  8. Sep 15, 2015 #7
    Thanks, I managed to find a solution to the problem with your explanation to the question.
     
  9. Sep 15, 2015 #8

    WWGD

    User Avatar
    Science Advisor
    Gold Member

    Nice geometric approach, RUBER, recognizing that the "bisecting" plane is in the solution set, much simpler than anything I had in mind.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Least Squares Approximation
  1. Least Squares (Replies: 1)

  2. Least squares (Replies: 8)

  3. Least Squares (Replies: 3)

Loading...