Re: [Help-gsl] Constraints for B-spline breakpoints

[Rhys Ulerich]

> I'm using the GSL B-spline functions to implement cubic spline smoothing.
>  My program is based on the example in the manual
> (http://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-B_002dsplines.html).
>
> I want to allow varying numbers of breakpoints (nbreak) to achieve different
> degrees of smoothing. The minimum nbreak for cubic splines is 2, but is
> there a maximum?

There should not be from the gsl_bspline routines.

>  If I use more than n-2 (where n is the number of data
> points), I get an error from "gsl_multifit_wlinear" when computing the
> spline coefficients:
> gsl: svd.c:236: ERROR: svd of MxN matrix, M<N, is not implemented
>
> For the offending fit matrix, M = n and N = ncoeffs = nbreak+k-2 = nbreak+2.

I'm not familiar with the svd routine.  Someone else will have to jump in here.

> Is there a way to use every (distinct location of a) data point as a
> breakpoint (via "gsl_bspline_knots")?

Yes, that should be possible if you get past the SVD constraint from above.
In that case you're just fitting a cubic spline interpolant and you may wish
to use http://www.gnu.org/software/gsl/manual/html_node/Interpolation.html

> Would it be possible to have more breakpoints than data points?

Probably, if you're working in a least squares sense.

> If so, would it make any sense to allow this?

I'm not sure that you'll gain anything.

- Rhys