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Adlil1-Visitor
1-Visitor
April 15, 2022
Solved

Where did I do wrong in in solving Least Square Method?

  • April 15, 2022
  • 3 replies
  • 2769 views

Hello PTC fam,
I don't know where did I do wrong in this programe.
the question is

Determine least square method value of coefficients Ci( i=0,...,m) in polynomial form.

Adlil_0-1650006616655.png


Calculate the approximation error  where m=3

Adlil_1-1650006637159.png

 



Please advice.
Regards,
Adlil

Best answer by LucMeekes

Did you mean to do this:

LucMeekes_0-1650015237550.png

Then:

LucMeekes_1-1650015833487.png

Finally:

LucMeekes_3-1650016354970.png

But there are options for minerr. If you press the right-mouse button on it, you can select other minimisation strategies. The above was done using 'Linear' (The default). For non-linear: Levenberg-Marquardt you may get:

LucMeekes_4-1650016487586.png

Success!
Luc

3 replies

L
LucMeekes23-Emerald IV
23-Emerald IV
April 15, 2022

Your sheet does not explain well what you are trying to achieve. Apart from that:

1. The summation for Toc in above picture goes from i=0 to m, when m=3, that means you should get C as a vector of 4 elements. Your sheet shows you calculate a vector C consisting of only three elements. The input for that calculation (matrix A and vector B) do not seem to be related to alpha or T.

2. Instead of the solve block, you can use the lsolve function to determine C from A and B:

LucMeekes_0-1650013718887.png

3. What is the vector K calculated for?

 

Success!
Luc

L
LucMeekes23-Emerald IVAnswer
23-Emerald IV
April 15, 2022

Did you mean to do this:

LucMeekes_0-1650015237550.png

Then:

LucMeekes_1-1650015833487.png

Finally:

LucMeekes_3-1650016354970.png

But there are options for minerr. If you press the right-mouse button on it, you can select other minimisation strategies. The above was done using 'Linear' (The default). For non-linear: Levenberg-Marquardt you may get:

LucMeekes_4-1650016487586.png

Success!
Luc

    A
    Adlil1-VisitorAuthor
    1-Visitor
    April 21, 2022

    Thank you for the reply. Pardon I should reconfirm back with you before hit the "accept the solution" button. I would like to ask 

    1. Does Gauss method is that simple ? Mind to explain why Gauss method we need to list like this compare to my version.
    2. What is Minerr function is ?
    3. Why do you sort vector T and alpha ?

    Sorry if my questions didn't look smart since I really want to understand this program and the task given. Thanks again waiting for your reply.

    Adlil_0-1650567939938.png

     

    F
    Fred_Kohlhepp23-Emerald I
    23-Emerald I
    April 16, 2022

    I've been playing with this.  A direct least squares fit to this data with a third order polynomial isn't great.  But a fourth order fit to the natural logs looks pretty good. (My apologies for diverting the discussion!)  Sheet in Prime 4.0 Express.

    Fred_Kohlhepp_0-1650111336924.png

     

      A
      Adlil1-VisitorAuthor
      1-Visitor
      April 21, 2022

      Thanks for the reply, didn't expect you achieve that close in the graph. Sadly I don't have Prime 4.0 appreciate for the help.

      W
      Werner_E25-Diamond I
      25-Diamond I
      April 21, 2022

      Here is a screenshot of Freds work (I just omitted the grid which can be achieved much easier in real Mathcad)

      Werner_E_2-1650570471928.png

       

      You can also create his function using Mathcads built-in polyfit function.
      Here a comparison of a rational fit (f1), a polynomial fit of fourth order (f2) and Freds approach (f3).

      According to the sum of squared errors the polynomial fit (f2) would win, but I bet you don't like the curve in the range from 2 to 5. So I guess that Freds approach rules.

      Werner_E_1-1650570381111.png

      MC15 sheet attached

       

       

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