What are some recommended textbooks for learning non-analytic curve fitting?

[mikeph]

Hi,

what are some good textbooks dedicated to this subject? I have a short time to learn everything about this subject (upto a certain level). I'm trying to fit a non-analytic curve (whose form I know) to some data.

edit- sorry, I don't only mean non-linear, I mean non-analytic. The curve is smoothly dependent on the parameter space so I don't expect it to be difficult, but it takes a computer to estimate its value. A human could do better than my current attempt at coding.

Thanks,

 

[disregardthat]

You can use linear algebra to find the "best" approximation to a set of data points using a linear combination of different functions. E.g. if you expect that a good approximation could be Ax+Bx^2+Csin(x), you can find constants A,B and C such that this function is optimized wrt your data points. More variables can also be used. This is treated in many books on linear algebra. E.g. Lay's.

 

[mikeph]

I know exactly what the function is, but it involves an integral that can only be calculated numerically. I'm seeking the parameters of this awkward function that causes it to best fit the data.

 

[Stephen Tashi]

I suggest you describe your problem completely.

 

[JJacquelin]

I know exactly what the function is, but it involves an integral that can only be calculated numerically.

If we knew what is the function and the form of the related integral, it might be possible to give a more pertinent answer.
Some examples involving numerical integration are provided in the paper "Régressions et Equations Intégrales" (not translated yet)
http://www.scribd.com/JJacquelin/documents