# I like Serena

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Showing Visitor Messages 1 to 10 of 100
1. Jan3-14 01:44 AM
Happy new year! :)

How's the new year treating you so far?
2. Jul10-13 12:37 AM
Shauheen
"Levenberg-Marquardt Algorithm for more than one function"

3. Jul9-13 03:03 AM
Shauheen
(Part 3/3)

How would be the formulation once two functions are involved?

I would really appreciate if you could help. It would be a tremendous help for me which I could receive through an expert in physics online forum.

Look forward to hearing from you.
All the bests,
Shauheen

PS: I was in Netherlands on the last week of June. It was a great time in TU Delft and Delft city. :)
4. Jul9-13 03:00 AM
Shauheen
(Part 2/3)

∇S(P)=2[-T(P)/∂P][Y-T(P)]=0

In which P is the vector of the unknown parameters, T is the model value vector and Y is the experimental value.
This problem, minimizes S(P)=Ʃ[Yi-Ti(P)]^2

Now, I have to find let say 3 parameters from the minimization of two errors from my experiments. In my experiment, I measure two values vs. time, let say Y and M. These two values are dependent. The number of the collected data are not the same for these two and I think they are both equally important. I could check on the typical range of errors to make them equally significant.
My question is how to minimize the error of the combination of these two and find my unknowns?

Let say if the error is like:
E(P)=Ʃ[Yi-Ti(P)]^2+Ʃ[Mi-Ui(P)]^2

Ui and Ti are the values from my model.
What would be the Jacobian matrix in this case? for one function, it would be like:
P(k+1)=P(k)+[(J(k)T.J(k)+μ(k)Ω(k)]^-1 (J(k))T[Y-T(P(k))]
in which k is the kth iteration.
5. Jul9-13 02:59 AM
Shauheen
(Part 1/3)

Hello I like Serena,

I have been looking how to use the Levenberg Marqurdt algorithm for minimizing the errors of two functions at the same time. I looked up this topic in the internet and the only useful thing I found was your guidance to thomas430 in summer 2011.

I read your notes, but still have problem in finding out how I have to calculate the Jacobian matrix.

I am measuring two values over time in the lab. Then, a numerical forward model has been developed which models the physics and now, I need to solve the inverse problem to find the unknown parameters. I have solved this problem previously several times when only one error function needed to be minimized. Based on what I have learned about LMA (from Inverse Heat Transfer by Necati Ozicik), the gradient of the error (from one function) will result in multiplication of the Jacobian matrix by the difference between the experimental and model results. This gradient needs to become zero:
6. Apr29-13 03:32 PM
ArcanaNoir
More so than last semester :)
7. Jan23-13 02:06 PM
ArcanaNoir
Hello! Haven't finished, been swamped! Last semester took 5 classes, sat in on 2, joined a research team, applied to grad schools, etc. This semester have 3 classes, sittting on 2, (4/5 graduate level), doing research for research team. I also haven't needed any homework help from the forum, on account of being in school full time so I have access to my classmates. I'm hoping to have some time to spend around the forum this semester. :)
8. Jan1-13 03:53 AM
sparkle123
Happy New Year!!!! :D All the best to you in 2013!
9. Nov28-12 05:44 PM
HeLiXe
Well I did some optics but had to drop the class and am finishing modern physics :)
10. Nov13-12 09:05 PM
Hey ILS,

I felt home.

Country
Netherlands
Educational Background
Master's
Degree in
MS computer science & mathematics, BS physics
Favorite Area of Science
All of them, preferably involving formulas
Profession
Software Engineer & Private tutor

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