RUS  ENG
Full version
JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2019 Volume 25, Number 2, Pages 205–219 (Mi timm1637)

This article is cited in 2 papers

A Method for the Construction of Local Parabolic Splines with Additional Knots

Yu. N. Subbotin, V. T. Shevaldin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

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 $W_{\infty}^2$ and $W_{\infty}^3$ by these splines in the uniform metric and calculate the exact uniform Lebesgue constants and the norms of the second derivatives on the class $W_{\infty}^2$. These properties are compared with the corresponding properties of Subbotin's splines.

Keywords: local parabolic splines, approximation, interpolation, equally spaced knots.

UDC: 519.65

MSC: 41A15

Received: 08.02.2019

DOI: 10.21538/0134-4889-2019-25-2-205-219


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2020, 309, suppl. 1, S151–S166

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024