On spline approximation with a reproducing kernel method
A.I. Rozhenko, T.S. Shaidorov
Keywords: spline, reproducing kernel, trend, radial basis function, external drift
Abstract
Spline approximation with a reproducing kernel of a semi-Hilbert space is studied. Conditions are formulated that uniquely identify the natural Hilbert space by a reproducing kernel, a trend of spline, and the approximation domain. The construction of spline with external drift is proposed. It allows one to approximate functions having areas of big gradients or first-kind breaks. The conditional positive definiteness of some known radial basis functions is proved.
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