[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## Re: [Help-gsl] Question on Bsplines knot multiplicity

**From**: |
Rhys Ulerich |

**Subject**: |
Re: [Help-gsl] Question on Bsplines knot multiplicity |

**Date**: |
Wed, 9 Jul 2014 08:40:39 -0500 |

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