Improve least squares solution

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carlos g 2018-7-17

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https://ww2.mathworks.cn/matlabcentral/answers/410750-improve-least-squares-solution

评论： dpb 2018-7-17

I have to solve a least squares problem in which y=Ax, where y is a vector whose entries are experimental data, A is my model and x is the solution I need to find so as to weight properly my model to fit the experiments. The following figure shows in blue the experimental data (y) and in red Ax.

How could I obtain a better fit for my data in MATLAB? Is there any specific function for this? (I am not sure how to use the nonlinear least squares method, I simply solved the normal equations with the backslash \ )

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carlos g 2018-7-17

The condition number is cond(A)=9.52911699912484e+18. Basically Ax has to fix y (the blue curve), so my question is basically if MATLAB has more powerful regression methods than the usual backslash (least squares) or if there is any trick I can use to overcome this bad result.

dpb 2018-7-17

You're apparently trying to use an extremely high-order polynomial to fit a very difficult problem.

The solution is undoubtedly to find a more suitable model.

The backslash operator is quite sophisticated despite its deceptively simple syntax; internally it does quite sophisticated stuff and generally outperforms any other technique for badly condition systems.

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