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Next: <a href="Example-programs-for-B_002dsplines.html#Example-programs-for-B_002dsplines" accesskey="n" rel="next">Example programs for B-splines</a>, Previous: <a href="Evaluation-of-B_002dspline-basis-function-derivatives.html#Evaluation-of-B_002dspline-basis-function-derivatives" accesskey="p" rel="previous">Evaluation of B-spline basis function derivatives</a>, Up: <a href="Basis-Splines.html#Basis-Splines" accesskey="u" rel="up">Basis Splines</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Working-with-the-Greville-abscissae-1"></a>
<h3 class="section">40.6 Working with the Greville abscissae</h3>
<a name="index-basis-splines_002c-Greville-abscissae"></a>
<a name="index-basis-splines_002c-Marsden_002dSchoenberg-points"></a>

<p>The Greville abscissae are defined to be the mean location of <em>k-1</em>
consecutive knots in the knot vector for each basis spline function of order
<em>k</em>.  With the first and last knots in the <code>gsl_bspline_workspace</code>
knot vector excluded, there are <code>gsl_bspline_ncoeffs</code> 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.
</p>
<dl>
<dt><a name="index-gsl_005fbspline_005fgreville_005fabscissa"></a>Function: <em>double</em> <strong>gsl_bspline_greville_abscissa</strong> <em>(size_t <var>i</var>, gsl_bspline_workspace *<var>w</var>);</em></dt>
<dd><p>Returns the location of the <em>i</em>-th Greville abscissa for the given
B-spline basis.  For the ill-defined case when <em>k=1</em>, the implementation
chooses to return breakpoint interval midpoints.
</p></dd></dl>





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