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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 8, Pages 1457–1471 (Mi zvmmf9698)  

This article is cited in 7 scientific papers (total in 7 papers)

Continuation of solutions in multiparameter approximation of curves and surfaces

E. B. Kuznetsov

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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:8, 1149–1162

Bibliographic databases:

UDC: 519.674
Received: 02.02.2012

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

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. 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  mathnet  crossref  crossref  isi  elib
    3. A. A. Semenov, “Strength and stability of geometrically nonlinear orthotropic shell structures”, Thin-Walled Struct., 106 (2016), 428–436  crossref  isi  elib  scopus
    4. 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  crossref  isi  scopus
    5. 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  mathnet  crossref  crossref  mathscinet  elib
    6. 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  crossref  crossref  isi  elib  scopus
    7. V. V. Karpov, “Models of the shells having ribs, reinforcement plates and cutouts”, Int. J. Solids Struct., 146 (2018), 117–135  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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