forum.alglib.net

Dear Sergey,

first I want to take the opportunity an gratulate you on ALGLIB, a great library, extremely clean coding style, very efficient.
Great work, a good programmer :)

I have only one simple question: when using linear interpolation (it is in fact polynomial regression, most of the values in the function
matrix are powers of >some x<), I encounter the issue that when increasing the number of equations (degrees of freedom in my model) over
a certain limit, often about 5 * 20 equations (means 5 sub-matrices with x^0 - x^20), the overall error starts to increase again.

Is it likely to be related to floating point / IEEE754 issues? I would guess so.

Best Regards :)

Almost surely, it is floating point issue. Polynomial basis is ill-conditioned, and having x^20 as basis function will give you very badly conditioned matrix. You can check fitting report, in particular - rep.taskrcond variable. If it is lower than 10^(-10), than you definitely have problems with condition number.

I recommend you to switch to better basis - for example, to replace x^i with centered Chebyshev polynomials.

Thank You for your time!

The polyfit function seems to give much better results for fitting high order polynomials than the least squares functions.

See an Excel implementation and examples here:

http://newtonexcelbach.wordpress.com/20 ... functions/

_________________
Doug Jenkins
http://newtonexcelbach.wordpress.com/

Doug, I'm aware. The polynomial fitting uses a barycentric method. However, not all equations in my model are polynomials.

Polynomial fitting uses Chebyshev basis internally, it just converts results into barycentric form before output.


I've recommended you to use Chebyshev polynomials as basis because you can use it with non-polynomial basis functions.

Thanks again, I have looked at the matrix condition and I'm using now Chebychev Polynomials with -1 <= x <= +1