Yu. S. Volkov, Yu. N. Subbotin, “50 years to Schoenberg's problem on the convergence of spline interpolation”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 52–67; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 222

Trudy Instituta Matematiki i Mekhaniki UrO RAN

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 1, Pages 52–67 (Mi timm1029)

This article is cited in 18 scientific papers (total in 18 papers)

50 years to Schoenberg's problem on the convergence of spline interpolation

Yu. S. Volkov^ab, Yu. N. Subbotin^cd

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University
^c Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^d Institute of Mathematics and Computer Science, Ural Federal University

Full-text PDF (228 kB) Citations (18)

References:

PDF

HTML

Abstract: A review of results on the convergence of interpolation process for polynomial splines and derivatives in the last 50 years is given.

Keywords: polynomial splines, interpolation, convergence.

Received: 30.08.2013

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 288, Issue 1, Pages 222–237
DOI: https://doi.org/10.1134/S0081543815020236

Bibliographic databases:

Document Type: Article

UDC: 517.518

Language: Russian

Citation: Yu. S. Volkov, Yu. N. Subbotin, “50 years to Schoenberg's problem on the convergence of spline interpolation”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 52–67; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 222–237

Citation in format AMSBIB

\Bibitem{VolSub14}

\by Yu.~S.~Volkov, Yu.~N.~Subbotin

\paper 50~years to Schoenberg's problem on the convergence of spline interpolation

\serial Trudy Inst. Mat. i Mekh. UrO RAN

\yr 2014

\vol 20

\issue 1

\pages 52--67

\mathnet{http://mi.mathnet.ru/timm1029}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364191}

\elib{https://elibrary.ru/item.asp?id=21258482}

\transl

\jour Proc. Steklov Inst. Math. (Suppl.)

\yr 2015

\vol 288

\issue , suppl. 1

\pages 222--237

\crossref{https://doi.org/10.1134/S0081543815020236}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000352991400022}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84958292260}

Linking options:

https://www.mathnet.ru/eng/timm1029

https://www.mathnet.ru/eng/timm/v20/i1/p52

This publication is cited in the following 18 articles:

Yu. S. Volkov, V. V. Bogdanov, “Estimates of the p-Norms of Solutions and Inverse Matrices of Systems of Linear Equations with a Circulant Matrix”, Comput. Math. and Math. Phys., 64:8 (2024), 1680
Yu. S. Volkov, “Estimates of the $p$-norms of solutions to difference equations and infinite systems of linear equations”, Siberian Math. J., 65:6 (2024), 1327–1335
Yu. S. Volkov, S. I. Novikov, “Estimates of solutions to infinite systems of linear equations and the problem of interpolation by cubic splines on the real line”, Siberian Math. J., 63:4 (2022), 677–690
Yuriy S. Volkov, Sergey I. Novikov, “Estimates for solutions of bi-infinite systems of linear equations”, European Journal of Mathematics, 8:2 (2022), 722
E. K. Kulikov, A. A. Makarov, “O postroenii approksimatsionnykh funktsionalov dlya minimalnykh splainov”, Chislennye metody i voprosy organizatsii vychislenii. XXXIV, Zap. nauchn. sem. POMI, 504, POMI, SPb., 2021, 136–156
Yu. S. Volkov, V. V. Bogdanov, “On error estimates of local approximation by splines”, Siberian Math. J., 61:5 (2020), 795–802
Yu. S. Volkov, “Mnogochleny Eilera v zadache ekstremalnoi funktsionalnoi interpolyatsii v srednem”, Tr. IMM UrO RAN, 26, no. 4, 2020, 83–97
Yu. S. Volkov, “One problem of extremal functional interpolation and the Favard constants”, Dokl. Math., 102:3 (2020), 474–477
Volkov Yu.S., “Efficient Computation of Favard Constants and Their Connection to Euler Polynomials and Numbers”, Sib. Electron. Math. Rep., 17 (2020), 1921–1942
Yong Yi Bay, Daniel J. Bodony, Jonathan B. Freund, “Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence”, Journal of Computational Physics, 419 (2020), 109680
Yu. S. Volkov, “Convergence of spline interpolation processes and conditionality of systems of equations for spline construction”, Sb. Math., 210:4 (2019), 550–564
V. V. Bogdanov, Yu. S. Volkov, “Shape-preservation conditions for cubic spline interpolation”, Siberian Adv. Math., 29:4 (2019), 231–262
Yu. S. Volkov, “Study of the convergence of interpolation processes with splines of even degree”, Siberian Math. J., 60:6 (2019), 973–983
V. N. Parakhina, P. N. Timoshenko, A. A. Simonov, M. A. Chernyshov, “Splinemodels in forecasting the balance of development of the industrial complex”, International Scientific and Practical Conference Contemporary Issues of Economic Development of Russia: Challenges and Opportunities, European Proceedings of Social and Behavioural Sciences, 59, ed. T. Alexandrovich, Future Acad, 2019, 657–667
Yu. S. Volkov, “Convergence of Quartic Interpolating Splines”, Proc. Steklov Inst. Math. (Suppl.), 308:1 (2020), S196–S202
V. T. Shevaldin, O. Ya. Shevaldina, “The Lebesgue constant of local cubic splines with equally-spaced knots”, Num. Anal. Appl., 10:4 (2017), 362–367
Yu. S. Volkov, “The general problem of polynomial spline interpolation”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 187–198
A. V. Chernov, “O kusochno postoyannoi approksimatsii v raspredelennykh zadachakh optimizatsii”, Tr. IMM UrO RAN, 21, no. 1, 2015, 264–279

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

Statistics & downloads:
Abstract page:	606
Full-text PDF :	142
References:	80
First page:	20

Registration to the website

Logotypes