Linear Model with 4 parameters

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?

[Alex Sha]

Show the data and the code your have written

[Torsten]

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.

Answer 1

[Matt J]

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{:});