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

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

Journal

Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802

Output data

Year: 2019, Volume: 210, Number: 4, Pages: 550-564 Pages count : 15 DOI: 10.1070/SM8964

Tags

Conditionality; Construction algorithms; Convergence; Interpolation; Projector norm; Splines

Authors

Volkov Yu.S. ^1,2

Affiliations

1	Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russian Federation
2	Novosibirsk State University, Novosibirsk, Russian Federation

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 kth derivative in B-splines is equivalent to the problem of convergence of the interpolation process for the Kth spline derivative in the class of functions with continuous Kth 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. © 2019 Turpion Ltd. All rights reserved.

Volkov Y.S.
Convergence of spline interpolation processes and conditionality of systems of equations for spline construction
Sbornik Mathematics. 2019. V.210. N4. P.550-564. DOI: 10.1070/SM8964 WOS Scopus РИНЦ OpenAlex

Волков Ю.С.
Сходимость процессов сплайн-интерполяции и обусловленность систем уравнений построения сплайнов
Математический сборник. 2019. Т.210. №4. С.87-102. DOI: 10.4213/sm8964 РИНЦ OpenAlex

Submitted:

May 5, 2017

≡ Web of science:	WOS:000471828000004
≡ Scopus:	2-s2.0-85071112315
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