Abstract:
We propose a general method for the construction of local parabolic splines with an arbitrary arrangement of knots for functions given on grid subsets of the number axis or its segment. Special cases of this scheme are Yu. N. Subbotin's and B. I. Kvasov's splines. For Kvasov's splines, we consider boundary conditions different from those suggested by Kvasov. We study the approximating and smoothing properties of these splines in the case of uniform knots. In particular, we find two-sided estimates for the error of approximation of the function classes W2∞ and W3∞ by these splines in the uniform metric and calculate the exact uniform Lebesgue constants and the norms of the second derivatives on the class W2∞. These properties are compared with the corresponding properties of Subbotin's splines.
Keywords:
local parabolic splines, approximation, interpolation, equally spaced knots.
Citation:
Yu. N. Subbotin, V. T. Shevaldin, “A Method for the Construction of Local Parabolic Splines with Additional Knots”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 2, 2019, 205–219; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S151–S166
\Bibitem{SubShe19}
\by Yu.~N.~Subbotin, V.~T.~Shevaldin
\paper A Method for the Construction of Local Parabolic Splines with Additional Knots
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 2
\pages 205--219
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\crossref{https://doi.org/10.21538/0134-4889-2019-25-2-205-219}
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2020
\vol 309
\issue , suppl. 1
\pages S151--S166
\crossref{https://doi.org/10.1134/S0081543820040173}
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Linking options:
https://www.mathnet.ru/eng/timm1637
https://www.mathnet.ru/eng/timm/v25/i2/p205
This publication is cited in the following 2 articles:
V. T. Shevaldin, “On Favard local parabolic interpolating splines with additional knots”, Comput. Math. Math. Phys., 63:6 (2023), 1045–1051
N. Varun Mathur, S. Bahadur, P. Mathur, “Approximation of non-interpolatory complex parabolic spline on the unit circle”, Filomat, 35:10 (2021), 3549–3556