How to do Linearization for Non-linear least squares?

In summary, linearization in non-linear least squares is a method used to approximate non-linear functions with linear ones by taking the first derivative of the non-linear function. It is important because it allows for the use of linear regression techniques and improves accuracy. To perform linearization, the non-linear function must be identified and its first derivative used to create a linear equation. However, linearization has limitations, such as only working well for approximately linear functions and not being suitable for highly curved or skewed data. Alternative methods, such as gradient descent and the Gauss-Newton method, may be more accurate for highly non-linear functions, but they can be more computationally intensive. The choice of method should take into account the characteristics of the data and the non
  • #1
artiny
7
0
Hy
I want to know how to make linearization for some function,...what should by in Non-linear least squares problems.
In my book I have only this example how to do:

http://i.imgur.com/MUFiHkr.pngSomeone could me help how to do, some receipt of method what I need to do?

Non-linear least squares problems was in Matlab:
x = [ 1 2 3 4 5]
y = [ 3.5 2 4 8]

u = log(y)
v = [ones(5,1), x']
btr = x\u'
beta0
...
...
fminsearch
 
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  • #2
You have more x data values than corresponding y values?
 

1. What is linearization in non-linear least squares?

Linearization in non-linear least squares is a method used to approximate a non-linear function with a linear one. This is done by taking the first derivative of the non-linear function and using it to create a linear equation that can be solved using traditional least squares methods.

2. Why is linearization important in non-linear least squares?

Linearization is important in non-linear least squares because it allows for the use of linear regression techniques, which are more straightforward and easier to solve than non-linear regression methods. It also helps to improve the accuracy of the estimates obtained from the non-linear model.

3. How do you perform linearization for non-linear least squares?

To perform linearization for non-linear least squares, you first need to identify the non-linear function that you want to approximate. Then, take the first derivative of the function and use it to create a linear equation. This equation can then be solved using traditional least squares methods to obtain estimates for the parameters of the non-linear function.

4. What are the limitations of linearization in non-linear least squares?

One limitation of linearization in non-linear least squares is that it only works well for functions that are approximately linear in the region of interest. If the non-linear function is highly curved, the linear approximation may not be accurate. Additionally, linearization may not be appropriate if the function has multiple local minima or if the data is highly skewed.

5. Are there any alternative methods to linearization for non-linear least squares?

Yes, there are alternative methods to linearization for non-linear least squares, such as gradient descent or the Gauss-Newton method. These methods are more computationally intensive but may be more accurate for highly non-linear functions. It is important to consider the characteristics of the data and the specific non-linear function when choosing the most appropriate method.

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