Linear Model with 4 parameters

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Robert Demyanovich
Robert Demyanovich 2022-2-28
评论： Torsten 2022-2-28
I need to come up with an estimate for the starting values of the coefficients of a rational model. The rational model is:
One source says that I could do this by performing a linear fit on the model:
I'm using Matlab to fit the rational model, but it performs poorly if I don't use good starting points for the coefficients.
How can I use Matlab to perform this linear regression on 4 data points in order to get starting values for A0, A1, B1 and B2?
  2 个评论
Alex Sha
Alex Sha 2022-2-28
Show the data and the code your have written
Torsten
Torsten 2022-2-28
If you only have 4 data points, then the best fit parameters to the linear model will in most cases already be the best-fit parameters to the rational model. This is because you usually get a unique solution for 4 equations in 4 unknowns.

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回答（1 个）

Matt J
Matt J 2022-2-28
编辑：Matt J 2022-2-28
Asssuming x and y are column vectors,
Q= [x.^0, x, -x.*y, -x.^2.*y,-y];
[~,~,V]=svd(Q,0);
coeffs=num2cell( V(:1:4)/V(end) );
[A0,A1,B1,B2]=deal(coeffs{:});

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