This article is cited in 3 papers

On spline approximation with a reproducing kernel method

A. I. Rozhenko^ab, T. S. Shaidorov<sup>c

a</sup> Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
^c ARS TERM, Krasnyi pr. 220, Novosibirsk, 630000, Russia

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.

Key words: spline, reproducing kernel, trend, radial basis function, external drift.

UDC: 517.972.5+519.65

Received: 13.11.2012
Revised: 22.03.2013

 English version: Numerical Analysis and Applications, 2013, 6:4, 314–323

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