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This article is cited in 5 scientific papers (total in 5 papers)
Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a differential operator
E. V. Strelkova, V. T. Shevaldin
Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
We construct local $\mathcal L$-splines with uniform nodes that preserve subsets from the kernel of a linear differential operator $\mathcal L$ of order $r$ with constant real coefficients and pairwise distinct roots of the characteristic polynomial. Pointwise estimates are found for the error of approximation by the constructed $\mathcal L$-splines on classes of functions defined by differential operators of orders smaller than $r$.
Keywords:
approximation, local $\mathcal L$-splines, differential operator.
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Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 273, suppl. 1, S133–S141
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UDC:
519.65
Received: 01.02.2010
Citation:
E. V. Strelkova, V. T. Shevaldin, “Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a differential operator”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 272–280; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S133–S141
Citation in format AMSBIB
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\vol 16
\issue 4
\pages 272--280
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http://mi.mathnet.ru/eng/timm661 http://mi.mathnet.ru/eng/timm/v16/i4/p272
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This publication is cited in the following articles:
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E. V. Strelkova, V. T. Shevaldin, “Form preservation under approximation by local exponential splines of an arbitrary order”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 171–179
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Yu. S. Volkov, E. G. Pytkeev, V. T. Shevaldin, “Orders of approximation by local exponential splines”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 175–184
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E. V. Strelkova, V. T. Shevaldin, “Local exponential splines with arbitrary knots”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 189–194
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E. V. Strelkova, V. T. Shevaldin, “On uniform Lebesgue constants of local exponential splines with equidistant knots”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 206–217
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E. V. Strelkova, V. T. Shevaldin, “O ravnomernykh konstantakh Lebega lokalnykh trigonometricheskikh splainov tretego poryadka”, Tr. IMM UrO RAN, 22, no. 2, 2016, 245–254
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