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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 4, Pages 156–165 (Mi timm650)  

Approximation by third-order local $\mathcal L$-splines with uniform nodes

P. G. Zhdanova, V. T. Shevaldinb

a Ural State University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: For a third-order linear differential operator of the form $\mathcal L_3=(D-\beta)(D-\gamma)(D-\delta)$ ($D$ is the differentiation symbol and $\beta,\gamma$, and $\delta$ are pairwise distinct real numbers) on the class of functions $W_\infty^{\mathcal L_2}$, where $\mathcal L_2=(D-\beta)(D-\gamma)$, a sharp pointwise estimate is found for the error of approximation by local noninterpolational $\mathcal L$- spines with uniform nodes corresponding to the operator $\mathcal L_3$; these splines were constructed by the authors earlier.

Keywords: approximation, local $\mathcal L$-splines, uniform nodes.

Full text: PDF file (170 kB)
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UDC: 517.5
Received: 01.02.2010

Citation: P. G. Zhdanov, V. T. Shevaldin, “Approximation by third-order local $\mathcal L$-splines with uniform nodes”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 156–165

Citation in format AMSBIB
\Bibitem{ZhdShe10}
\by P.~G.~Zhdanov, V.~T.~Shevaldin
\paper Approximation by third-order local $\mathcal L$-splines with uniform nodes
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 4
\pages 156--165
\mathnet{http://mi.mathnet.ru/timm650}
\elib{https://elibrary.ru/item.asp?id=15318497}


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