How can I fit the roots of a polynomial function?

My data can be model as a solution (a root) of a polynomial function. I have a set of (x,y) data that can be model as y^3+(1-k*x)*y^2+2y+1=0 and I want to fit the parameter k. My (x,y) data are one of the solution of this function. How can I do it? And in case for a generic n-th degree polynomial?

Answer 1

[Torsten]

Use lsqnonlin with fun = @(k)ydata.^3+(1-k(1)*xdata).*ydata.^2+2*ydata+1.

Best wishes

Torsten.

[Edoardo Vicentini]

Can I do it also with multiple parameter? k1,k2....

[Torsten]

You mean that your model equation has several parameters ki to be fitted ?

Yes, you can.

[Edoardo Vicentini]

Yes. 3 parameter to be fitted