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

This article is cited in 5 scientific papers (total in 5 papers)

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
Received: 25.05.2006

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  mathnet  crossref
    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  mathnet  elib
    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  mathnet  crossref  isi  elib
    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  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
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