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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 12, Pages 2129–2140 (Mi zvmmf68)  

This article is cited in 8 scientific papers (total in 8 papers)

On the best parametrization

E. B. Kuznetsov

Moscow Aviation Institute (State University), sh. Volokolamskoe 4, Moscow, 125993, Russia

Abstract: The numerical solution to a system of nonlinear algebraic or transcendental equations with several parameters is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are proved for choosing the best parameters, which provide the best condition number for the system of linear continuation equations. Such parameters have to be sought in the subspace tangent to the solution space of the system of nonlinear equations. This subspace is obtained if the original system of nonlinear equations is solved at the various parameter values from a given set. The parametric approximation of curves and surfaces is considered.

Key words: system of nonlinear equations with parameters, best parameters, best parametrization of curves and surfaces.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:12, 2162–2171

Bibliographic databases:

UDC: 519.62
Received: 15.11.2007

Citation: E. B. Kuznetsov, “On the best parametrization”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2129–2140; Comput. Math. Math. Phys., 48:12 (2008), 2162–2171

Citation in format AMSBIB
\by E.~B.~Kuznetsov
\paper On the best parametrization
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 12
\pages 2129--2140
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 12
\pages 2162--2171

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    This publication is cited in the following articles:
    1. E. B. Kuznetsov, “Multidimensional parametrization and numerical solution of systems of nonlinear equations”, Comput. Math. Math. Phys., 50:2 (2010), 244–255  mathnet  crossref  mathscinet  adsnasa  isi
    2. E. B. Kuznetsov, “Continuation of solutions in multiparameter approximation of curves and surfaces”, Comput. Math. Math. Phys., 52:8 (2012), 1149–1162  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Syresin D.E., Zharnikov T.V., Tyutekin V.V., “Dispersion properties of helical waves in radially inhomogeneous elastic media”, J. Acoust. Soc. Am., 131:6 (2012), 4263–4271  crossref  adsnasa  isi  elib  scopus
    4. Syresin D., Zharnikov T., “An algorithm to calculate dispersion properties of helical waves in radially inhomogeneous elastic waveguides”, International Congress on Ultrasonics (Gdansk, 2011), AIP Conf. Proc., 1433, eds. Linde B., Paczkowski J., Ponikwicki N., Amer. Inst. Physics, 2012, 451–454  crossref  adsnasa  isi  scopus
    5. Zharnikov T.V., Syresin D.E., “Formulation of the Riccati Equation For the Impedance Operator in Cylindrical Coordinates For Inhomogeneous Anisotropic Waveguides With the Example of Rectilinear Anisotropy”, Wave Motion, 52 (2015), 1–14  crossref  mathscinet  isi  elib  scopus
    6. 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
    7. 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
    8. E. B. Kuznetsov, S. S. Leonov, “Parametrization of the Cauchy problem for systems of ordinary differential equations with limiting singular points”, Comput. Math. Math. Phys., 57:6 (2017), 931–952  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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