E. B. Kuznetsov, “Continuation of solutions in multiparameter approximation of curves and surfaces”, Zh. Vychisl. Mat. Mat. Fiz., 52:8 (2012), 1457–1471; Comput. Math. Math. Phys., 52:8 (2012), 1149

Loading [MathJax]/jax/output/SVG/config.js

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki

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

Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
	Find

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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 8, Pages 1457–1471 (Mi zvmmf9698)

This article is cited in 9 scientific papers (total in 9 papers)

Continuation of solutions in multiparameter approximation of curves and surfaces

E. B. Kuznetsov

Moscow State Aviation Institute, Volokolamskoe sh. 4, Moscow, 125993 Russia

Full-text PDF (284 kB) Citations (9)

References:

PDF

HTML

Abstract: When a system of nonlinear algebraic or transcendental equations with several parameters is solved numerically, the best parameters within the framework of the continuation method have to be sought in the tangent space of the solution set of this system. More specifically, these parameters have to be sought in the directions of the eigenvectors of a linear self-adjoint transformation. Algorithms for the best parametrization of curves and surfaces are proposed. Numerical examples of parametric interpolation of surfaces confirm previously known theoretical results.

Key words: parametric system of nonlinear equations, best parameters, splines, parametrization of curves, parametrization of surfaces.

Received: 02.02.2012

English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 8, Pages 1149–1162
DOI: https://doi.org/10.1134/S0965542512080076

Bibliographic databases:

Document Type: Article

UDC: 519.674

Language: Russian

Citation: E. B. Kuznetsov, “Continuation of solutions in multiparameter approximation of curves and surfaces”, Zh. Vychisl. Mat. Mat. Fiz., 52:8 (2012), 1457–1471; Comput. Math. Math. Phys., 52:8 (2012), 1149–1162

Citation in format AMSBIB

\Bibitem{Kuz12}

\by E.~B.~Kuznetsov

\paper Continuation of solutions in multiparameter approximation of curves and surfaces

\jour Zh. Vychisl. Mat. Mat. Fiz.

\yr 2012

\vol 52

\issue 8

\pages 1457--1471

\mathnet{http://mi.mathnet.ru/zvmmf9698}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3245238}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012CMMPh..52.1149K}

\elib{https://elibrary.ru/item.asp?id=17845619}

\transl

\jour Comput. Math. Math. Phys.

\yr 2012

\vol 52

\issue 8

\pages 1149--1162

\crossref{https://doi.org/10.1134/S0965542512080076}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000307883700007}

\elib{https://elibrary.ru/item.asp?id=20472040}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865528182}

Linking options:

https://www.mathnet.ru/eng/zvmmf9698

https://www.mathnet.ru/eng/zvmmf/v52/i8/p1457

This publication is cited in the following 9 articles:

Karpov V.V., Semenov A.A., “Structural Anisotropy Method For Shells With Orthogonal Stiffeners”, Structures, 34 (2021), 3206–3221
Karpov V.V., Semenov A.A., “Refined Model of Stiffened Shells”, Int. J. Solids Struct., 199 (2020), 43–56
Yu. V. Klochkov, A. P. Nikolaev, T. R. Ishchanov, “Allowance for transverse shear deformations in the finite element calculation of a thin elliptic cylinder shell”, J. Mach. Manuf. Reliab., 47:4 (2018), 349–355
V. V. Karpov, “Models of the shells having ribs, reinforcement plates and cutouts”, Int. J. Solids Struct., 146 (2018), 117–135
V. V. Karpov, A. A. Semenov, “Mathematical models and algorithms for studying the strength and stability of shell structures”, J. Appl. Industr. Math., 11:1 (2017), 70–81
S. D. Krasnikov, E. B. Kuznetsov, “Numerical continuation of solution at a singular point of high codimension for systems of nonlinear algebraic or transcendental equations”, Comput. Math. Math. Phys., 56:9 (2016), 1551–1564
A. A. Semenov, “Strength and stability of geometrically nonlinear orthotropic shell structures”, Thin-Walled Struct., 106 (2016), 428–436
V. Karpov, A. Semenov, “Comprehensive study of the strength and stability of shallow shells made of fiberglass”, Mechanics, Resource and Diagnostics of Materials and Structures, MRDMS-2016, Proceedings of the 10th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures (Ekaterinburg, Russia, 16?20 May 2016), AIP Conf. Proc., 1785, eds. E. Gorkunov, V. Panin, S. Ramasubbu, Amer. Inst. Phys., 2016, UNSP 040022
S. D. Krasnikov, E. B. Kuznetsov, “Numerical continuation of solution at singular points of codimension one”, Comput. Math. Math. Phys., 55:11 (2015), 1802–1822

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

Журнал вычислительной математики и математической физики

Computational Mathematics and Mathematical Physics

Statistics & downloads:
Abstract page:	507
Full-text PDF :	139
References:	98
First page:	14

Registration to the website

Logotypes