How to do Linearization for Non-linear least squares?

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SUMMARY

This discussion focuses on the process of linearization in the context of Non-linear Least Squares (NLS) problems, specifically using MATLAB. The user seeks guidance on applying linearization techniques to a given dataset, where the independent variable is defined as x = [1, 2, 3, 4, 5] and the dependent variable as y = [3.5, 2, 4, 8]. The discussion references the use of the logarithmic transformation of y (u = log(y)) and the construction of a design matrix (v = [ones(5,1), x']). The user also mentions the fminsearch function for optimization.

PREREQUISITES
  • Understanding of Non-linear Least Squares (NLS) problems
  • Familiarity with MATLAB programming
  • Knowledge of linearization techniques
  • Experience with optimization functions such as fminsearch
NEXT STEPS
  • Study the implementation of Non-linear Least Squares in MATLAB using the lsqcurvefit function
  • Learn about the Jacobian matrix and its role in linearization
  • Explore advanced optimization techniques in MATLAB, such as using the Optimization Toolbox
  • Investigate the effects of different transformations on data for linearization
USEFUL FOR

Data scientists, statisticians, and engineers working with Non-linear Least Squares problems in MATLAB who need to understand linearization techniques for model fitting.

artiny
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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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You have more x data values than corresponding y values?
 

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