Abstract:
In this paper with the help of parabolic splines we construct a linear method of approximate recovery of functions by their values on an arbitrary grid. In the method, a spline inherits the properties of monotonicity and convexity from the approximated function, and is sufficiently smooth. In addition, the constructed linear operator as an operator acting from the space of continuous functions to the same space has the norm equal to one. We also obtain similar results for trigonometric splines of third order.
Citation:
Yu. N. Subbotin, “Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 2, 2007, 156–166; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S231–S242
\Bibitem{Sub07}
\by Yu.~N.~Subbotin
\paper Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 2
\pages 156--166
\mathnet{http://mi.mathnet.ru/timm98}
\elib{https://elibrary.ru/item.asp?id=12040778}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2007
\vol 259
\issue , suppl. 2
\pages S231--S242
\crossref{https://doi.org/10.1134/S0081543807060168}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38949168215}
Linking options:
https://www.mathnet.ru/eng/timm98
https://www.mathnet.ru/eng/timm/v13/i2/p156
This publication is cited in the following 5 articles:
E. V. Strelkova, V. T. Shevaldin, “Local exponential splines with arbitrary knots”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 189–194
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
Yu. S. Volkov, V. T. Shevaldin, “Usloviya formosokhraneniya pri interpolyatsii splainami vtoroi stepeni po Subbotinu i po Marsdenu”, Tr. IMM UrO RAN, 18, no. 4, 2012, 145–152
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
E. V. Strelkova, V. T. Shevaldin, “Approximation by local 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
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