Quartic spliens with minimal norms. (English) Zbl 1044.41008

If univariate even degree splines are used to interpolate mean values or derivatives in lieu of function values, they may be shown to minimise certain Sobolev semi-norms. This is the usual analogy to the well-known odd-degree natural splines that interpolate function values while minimising Sobolev semi-norms. In the special case of quartic splines, this paper studies generalisation of these minimisation properties and addresses in particular existence and uniqueness of the generated splines.


41A15 Spline approximation
65D05 Numerical interpolation
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