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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2013, Volume 16, Number 4, Pages 365–376 (Mi sjvm524)  
This article is cited in 4 scientific papers (total in 4 papers)

On spline approximation with a reproducing kernel method

A. I. Rozhenkoab, T. S. Shaidorovc

a 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
Full-text PDF (490 kB) Citations (4)
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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.
Received: 13.11.2012
Revised: 22.03.2013
English version:
Numerical Analysis and Applications, 2013, Volume 6, Issue 4, Pages 314–323
DOI: https://doi.org/10.1134/S199542391304006X
Bibliographic databases:
Document Type: Article
UDC: 517.972.5+519.65
Language: Russian
Citation: A. I. Rozhenko, T. S. Shaidorov, “On spline approximation with a reproducing kernel method”, Sib. Zh. Vychisl. Mat., 16:4 (2013), 365–376; Num. Anal. Appl., 6:4 (2013), 314–323
Citation in format AMSBIB
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\by A.~I.~Rozhenko, T.~S.~Shaidorov
\paper On spline approximation with a~reproducing kernel method
\jour Sib. Zh. Vychisl. Mat.
\yr 2013
\vol 16
\issue 4
\pages 365--376
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\elib{https://elibrary.ru/item.asp?id=21897047}
\transl
\jour Num. Anal. Appl.
\yr 2013
\vol 6
\issue 4
\pages 314--323
\crossref{https://doi.org/10.1134/S199542391304006X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889059205}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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