Yu. S. Volkov, V. V. Bogdanov, V. L. Miroshnichenko, V. T. Shevaldin, “Shape-Preserving Interpolation by Cubic Splines”, Mat. Zametki, 88:6 (2010), 836–844; Math. Notes, 88:6 (2010), 798

Matematicheskie Zametki

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
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

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

Matematicheskie Zametki, 2010, Volume 88, Issue 6, Pages 836–844
DOI: https://doi.org/10.4213/mzm6576 (Mi mzm6576)

This article is cited in 20 scientific papers (total in 20 papers)

Shape-Preserving Interpolation by Cubic Splines

Yu. S. Volkov^ab, V. V. Bogdanov^a, V. L. Miroshnichenko^ab, V. T. Shevaldin^c

^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

Full-text PDF (451 kB) Citations (20)

References:

PDF

HTML

DOI: https://doi.org/10.4213/mzm6576

Abstract: We consider the problem of shape-preserving interpolation by cubic splines. We propose a unified approach to the derivation of sufficient conditions for the $k$‑monotonicity of splines (the preservation of the sign of any derivative) in interpolation of $k$-monotone data for $k=0,\dots,4$.

Keywords: cubic spline, shape-preserving interpolation, $k$‑monotonicity, $B$-spline, matrix with diagonal dominance.

Received: 01.11.2008

English version:
Mathematical Notes, 2010, Volume 88, Issue 6, Pages 798–805
DOI: https://doi.org/10.1134/S0001434610110209

Bibliographic databases:

Document Type: Article

UDC: 517.518.8

Language: Russian

Citation: Yu. S. Volkov, V. V. Bogdanov, V. L. Miroshnichenko, V. T. Shevaldin, “Shape-Preserving Interpolation by Cubic Splines”, Mat. Zametki, 88:6 (2010), 836–844; Math. Notes, 88:6 (2010), 798–805

Citation in format AMSBIB

\Bibitem{VolBogMir10}

\by Yu.~S.~Volkov, V.~V.~Bogdanov, V.~L.~Miroshnichenko, V.~T.~Shevaldin

\paper Shape-Preserving Interpolation by Cubic Splines

\jour Mat. Zametki

\yr 2010

\vol 88

\issue 6

\pages 836--844

\mathnet{http://mi.mathnet.ru/mzm6576}

\crossref{https://doi.org/10.4213/mzm6576}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2868407}

\transl

\jour Math. Notes

\yr 2010

\vol 88

\issue 6

\pages 798--805

\crossref{https://doi.org/10.1134/S0001434610110209}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000288489700020}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78651245173}

Linking options:

https://www.mathnet.ru/eng/mzm6576

https://doi.org/10.4213/mzm6576

https://www.mathnet.ru/eng/mzm/v88/i6/p836

This publication is cited in the following 20 articles:

Boontarika Saeloo, Kulpavee Jitapunkul, Pawin Iamprasertkun, Gasidit Panomsuwan, Weekit Sirisaksoontorn, Tawan Sooknoi, Wisit Hirunpinyopas, “Size-Dependent Graphene Support for Decorating Gold Nanoparticles as a Catalyst for Hydrogen Evolution Reaction with Machine Learning-Assisted Prediction”, ACS Appl. Mater. Interfaces, 2023
Jingyang Xia, Mengqi Chen, Weiguo Fang, “Air Combat Intention Recognition with Incomplete Information Based on Decision Tree and GRU Network”, Entropy, 25:4 (2023), 671
Yu. S. Volkov, “Shape Preserving Conditions for Integro Quadratic Spline Interpolation in the Mean”, Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S291–S297
Gangfeng Zheng, Hao Dong, Ze Li, Songfeng Liu, Bin Wu, Cunfu He, “Shape Reconstruction of Columnar Structure Defect”, Research in Nondestructive Evaluation, 33:6 (2022), 277
Bogdanov V.V. Volkov Yu.S., “Near-Optimal Tension Parameters in Convexity Preserving Interpolation By Generalized Cubic Splines”, Numer. Algorithms, 86:2 (2021), 833–861
Zhanlav T., Mijiddorj R., “Integro Cubic Splines on Non-Uniform Grids and Their Properties”, East Asian J. Appl. Math., 11:2 (2021), 406–420
Zheng Gangfeng, Wu Bolin, Li Ze, Liu Songfeng, Dong Hao, Zhang Haotian, “Three-Dimensional Reconstruction of a Shaft-Type Deep-Small Hole With Variable Aperture Based on Image Processing For Ultrasound Detection”, Insight, 63:4 (2021), 236–240
Yu. S. Volkov, V. V. Bogdanov, “On error estimates of local approximation by splines”, Siberian Math. J., 61:5 (2020), 795–802
V. V. Bogdanov, Yu. S. Volkov, “Shape-preservation conditions for cubic spline interpolation”, Siberian Adv. Math., 29:4 (2019), 231–262
V. A. Skorospelov, P. A. Turuk, “Geometric support of numerical simulation of flow in the region of the hydroturbine spiral case”, J. Appl. Industr. Math., 12:2 (2018), 355–361
A.-R. K. Ramazanov, V. G. Magomedova, “Kovypuklaya interpolyatsiya splainami po trekhtochechnym ratsionalnym interpolyantam”, Tr. IMM UrO RAN, 24, no. 3, 2018, 164–175
A.-R. K. Ramazanov, V. G. Magomedova, “Vypuklaya interpolyatsiya ratsionalnymi splain-funktsiyami klassa $C^2$”, Dagestanskie elektronnye matematicheskie izvestiya, 2018, no. 9, 62–67
A.-R. K. Ramazanov, V. G. Magomedova, “Kovypuklaya interpolyatsiya ratsionalnymi splain-funktsiyami po ravnomernym setkam uzlov”, Dagestanskie elektronnye matematicheskie izvestiya, 2018, no. 10, 13–22
A.-R. K. Ramazanov, V. G. Magomedova, “Ob usloviyakh vypuklosti splainov po trekhtochechnym ratsionalnym interpolyantam”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 1–6
V. V. Bogdanov, Yu. S. Volkov, “Ob usloviyakh formosokhraneniya pri interpolyatsii parabolicheskimi splainami po Subbotinu”, Tr. IMM UrO RAN, 22, no. 4, 2016, 102–113
S. P. Sidorov, Lecture Notes in Computer Science, 9582, Mathematical Aspects of Computer and Information Sciences, 2016, 93
V. V. Bogdanov, “Sufficient conditions for the nonnegativity of solutions to a system of equations with a nonstrictly jacobian matrix”, Siberian Math. J., 54:3 (2013), 425–430
Qu Jianling, Sun Wenzhu, Hao Shiyong, Zhou Yuping, Gao Feng, 2013 IEEE 11th International Conference on Electronic Measurement & Instruments, 2013, 1009
Yu. S. Volkov, V. T. Shevaldin, “Usloviya formosokhraneniya pri interpolyatsii splainami vtoroi stepeni po Subbotinu i po Marsdenu”, Tr. IMM UrO RAN, 18, no. 4, 2012, 145–152
Yu. S. Volkov, E. V. Strelkova, V. T. Shevaldin, “Local approximation by splines with displacement of nodes”, Siberian Adv. Math., 23:1 (2013), 69–75

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

Statistics & downloads:
Abstract page:	864
Full-text PDF :	442
References:	104
First page:	26

Registration to the website

Logotypes