Geodesic
On spline approximation with a~reproducing kernel method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 365-376

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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. 
@article{SJVM_2013_16_4_a5,
     author = {A. I. Rozhenko and T. S. Shaidorov},
     title = {On spline approximation with a~reproducing kernel method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {365--376},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2013_16_4_a5/}
}
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A. I. Rozhenko; T. S. Shaidorov. On spline approximation with a~reproducing kernel method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 365-376. http://geodesic.mathdoc.fr/item/SJVM_2013_16_4_a5/