GNU Scientific Library – Reference Manual: Working with the Greville abscissae

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### 39.6 Working with the Greville abscissae

The Greville abscissae are defined to be the mean location of k-1 consecutive knots in the knot vector for each basis spline function of order k. With the first and last knots in the `gsl_bspline_workspace` knot vector excluded, there are `gsl_bspline_ncoeffs` Greville abscissae for any given B-spline basis. These values are often used in B-spline collocation applications and may also be called Marsden-Schoenberg points.

Function: double gsl_bspline_greville_abscissa (size_t i, gsl_bspline_workspace *w);

  Returns the location of the i-th Greville abscissa for the given B-spline basis. For the ill-defined case when k=1, the implementation chooses to return breakpoint interval midpoints.