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Mat. Sb., 2019, Volume 210, Number 4, Pages 87–102 (Mi msb8964)  

Convergence of spline interpolation processes and conditionality of systems of equations for spline construction

Yu. S. Volkovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: This study is a continuation of research on the convergence of interpolation processes with classical polynomial splines of odd degree. It is proved that the problem of good conditionality of a system of equations for interpolation spline construction via coefficients of the expansion of the $k$th derivative in $B$-splines is equivalent to the problem of convergence of the interpolation process for the $k$th spline derivative in the class of functions with continuous $k$th derivatives. It is established that for interpolation with splines of degree $2n-1$, the conditions that the projectors corresponding to the derivatives of orders $k$ and $2n-1-k$ be bounded are equivalent.
Bibliography: 26 titles.

Keywords: splines, interpolation, convergence, projector norm, construction algorithms, conditionality.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2016-0013
Russian Foundation for Basic Research 15-07-07530-а
This study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences (project no. 0314-2016-0013) and was supported by the Russian Foundation for Basic Research (grant no. 15-07-07530-а).


DOI: https://doi.org/10.4213/sm8964

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English version:
Sbornik: Mathematics, 2019, 210:4, 550–564

Bibliographic databases:

UDC: 517.518.85
MSC: Primary 41A15; Secondary 65D07
Received: 05.05.2017 and 17.07.2018

Citation: Yu. S. Volkov, “Convergence of spline interpolation processes and conditionality of systems of equations for spline construction”, Mat. Sb., 210:4 (2019), 87–102; Sb. Math., 210:4 (2019), 550–564

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