• a.mlw.walker
In summary, the conversation is about a paper discussing equations for least squares minimization based on empirical data. The first equation (eqn 40) uses levenberg marquardt to minimize a, b, and c0, where k is a constant and t_k represents stored times. The second equation (eqn 41) freezes beta and uses the golden section method to refine a and b. The author also provides sub equations for c0. The third equation (eqn 42) uses the same method as the first two, but for nu, phi, and omega^2. The conversation also touches on the use of levenberg marquardt and the author's desire for discussion and understanding rather than just the answer
a.mlw.walker
Hi I have attached an image of part of a freely available paper I was reading. It shows the equations for least squares minimization of some equations based on empirical data.

I am not completely confident I understand the required steps, and therefore just wanted to talk it through with others, see what you say and see if it sparks any ideas to solve these.

As I understand it, the first equation (eqn 40) is minimizes using levenberg marquardt for a, b and c0. k is 1,2,3,4... t_k is times stored, the rest of the equation is trying to model the time it will take (whatever that time may be).

Ok so using levenberg marquardt estimate a, b and c0.
But the the next equation (eqn 41) says that he freezes beta to be ab^2, and uses golden section method to 'refine' a and b?

Did the leveneberg marquardt not do a good enough job because I thought we found and ab that way?

the author also give the sub equations for c0. Why? I thought we estimated c0?

Ok so however it has been done, we have a good estimate for a, b and c0.
Eqn 42. Same thing again except now for nu, phi, omega^2.

How is it explaining to solve this?
"robus linear estimation"? "Directly minimizing"? Is that how? Why can't we use levenberg marquardt again?

I just would like discussion, I am not after just the answer, I would like to understand when to use what, and why...

Thanks guys

By the way, that is the whole chapter I haven't left anything out except the chapter title

#### Attachments

• parameter estimation.jpg
21.3 KB · Views: 463
Last edited:
Is this in the wrong forum?

## 2. How can I make sure the advice I receive is reliable?

To ensure the advice you receive is reliable, it's important to seek advice from multiple sources and do your own research. Consider the credentials and expertise of the person giving the advice and use your own judgement to determine if the advice is sound.

## 3. Is it better to ask for advice from a professional or a friend?

This ultimately depends on the type of advice you need. If it is a complex or technical issue, it may be best to seek advice from a professional. However, if it is a personal or emotional issue, a friend may be able to provide more empathetic and understanding advice.

## 4. How do I show my gratitude for the advice I receive?

A simple thank you goes a long way in showing your gratitude for the advice you receive. You can also offer to return the favor in the future or provide updates on how the advice helped you.

If you receive conflicting advice, take the time to consider both perspectives and weigh the pros and cons. You can also seek additional opinions or do more research before making a decision.

• Other Physics Topics
Replies
2
Views
326
• Chemistry
Replies
131
Views
5K
• Introductory Physics Homework Help
Replies
8
Views
337
• Other Physics Topics
Replies
3
Views
1K
• Mechanical Engineering
Replies
34
Views
5K
• General Engineering
Replies
25
Views
14K
• Mechanics
Replies
45
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
• Atomic and Condensed Matter
Replies
4
Views
2K
• General Math
Replies
17
Views
5K