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 Trudy Inst. Mat. i Mekh. UrO RAN, 2006, Volume 12, Number 2, Pages 195–213 (Mi timm163)

Approximation by local $L$-splines corresponding to a linear differential operator of the second order

V. T. Shevaldin

Abstract: For the class of functions $W_\infty^{\mathcal L_2}=\{f:f'\in AC,\|\mathcal L_2(D)f\|_\infty\le1\}$, where $\mathcal L_2(D)$ is a linear differential operator of the second order whose characteristic polynomial has only real roots, we construct a noninterpolating linear positive method of exponential spline approximation possessing extremal and smoothing properties and locally inheriting the monotonicity of the initial data (the values of a function $f\in W_\infty^{\mathcal L_2}$ at the points of a uniform grid). The approximation error is calculated exactly for this class of functions in the uniform metric.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2006, 255, suppl. 2, S178–S197

Bibliographic databases:

UDC: 519.65

Citation: V. T. Shevaldin, “Approximation by local $L$-splines corresponding to a linear differential operator of the second order”, Control, stability, and inverse problems of dynamics, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 2, 2006, 195–213; Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S178–S197

Citation in format AMSBIB
\Bibitem{She06} \by V.~T.~Shevaldin \paper Approximation by local $L$-splines corresponding to a~linear differential operator of the second order \inbook Control, stability, and inverse problems of dynamics \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2006 \vol 12 \issue 2 \pages 195--213 \mathnet{http://mi.mathnet.ru/timm163} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338256} \zmath{https://zbmath.org/?q=an:1137.65049} \elib{https://elibrary.ru/item.asp?id=12040748} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2006 \vol 255 \issue , suppl. 2 \pages S178--S197 \crossref{https://doi.org/10.1134/S0081543806060150} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846965269} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. V. Shevaldina, “Local $\mathcal L$-splines preserving the differential operator kernel”, Num. Anal. Appl., 3:1 (2010), 90–99
2. P. G. Zhdanov, V. T. Shevaldin, “Approksimatsiya lokalnymi $\mathcal L$-splainami tretego poryadka s ravnomernymi uzlami”, Tr. IMM UrO RAN, 16, no. 4, 2010, 156–165
3. E. V. Strelkova, V. T. Shevaldin, “Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a differential operator”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S133–S141
4. Gosse L., “Viscous Equations Treated With l-Splines and Steklov-Poincaré Operator in Two Dimensions”, Innovative Algorithms and Analysis, Springer Indam Series, 16, eds. Gosse L., Natalini R., Springer International Publishing Ag, 2017, 167–195
5. Gosse L., “L-Splines and Viscosity Limits For Well-Balanced Schemes Acting on Linear Parabolic Equations”, Acta Appl. Math., 153:1 (2018), 101–124
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