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Optimal interpolatory splines using \(B\)-spline representation. (English) Zbl 1068.41017
The purpose of this paper is a generalisation of the concept of minimal norm splines and natural splines, i.e. splines that minimise certain Sobolev semi-norms. General univariate polynomial splines are considered, and using a \(B\)-spline basis, the existence and certain splines minimising Sobolev norms is established. For instance, the unique existence of optimal spline interpolants is characterised in terms of the knots of the splines.

41A15 Spline approximation
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65D05 Numerical interpolation
65D07 Numerical computation using splines
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