Hi Foivos, > this is just to verify mainly, it is in my understanding that the sequence > of breakpoints is non decreasing (but not strictly), i.e. > > \xi_1 <= \xi_2 <= ... <= \xi_n. > > thus intermediate breakpoints can have some multiplicity (say, if we allow > some of them to be equal).
Yes, in for general B-spline theory the sequence of breakpoints only need be increasing, not strictly increasing. People tend to refer to them as a "knot" sequence in that setting. Repeated knots reduce local continuity in the basis. As far as a I know, when people use "breakpoint" they tend to mean a strictly increasing sequence producing a basis with the same continuity everywhere. > Could please someone verify that GSL support > this (I see it working - just for me ease of mind)? I don't know about "support". Certainly the PPPACK routines on which the B-splines in the GSL are built should handle this correctly. But I'd suspect there may be edge cases in the code because, as far as I know, they were intended for "breakpoints" and not more general "knots". That said, it may all work fine. Any contributions you wish to make in this regard would be much appreciated. - Rhys
