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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 11, Pages 1923–1949 (Mi zvmmf376)  

This article is cited in 1 scientific paper (total in 1 paper)

Fast automatic differentiation as applied to the computation of second derivatives of composite functions

E. S. Zasukhina

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
References:
Abstract: A technique for deriving formulas for the second derivatives of a composite function with constrained variables is proposed. The original system of constraint equations is associated with a linear system of equations, whose solution is used to determine the Hessian of the function. The resulting formulas are applied to discrete problems obtained by approximating optimal control problems with the use of Runge–Kutta methods of various orders. For a particular optimal control problem, the numerical results obtained by the gradient method and Newton's method with the resulting formulas are described and analyzed in detail.
Key words: fast automatic differentiation (FAD), Lagrangian, Euler scheme, Runge–Kutta method, splines.
Received: 05.05.2006
Revised: 31.05.2006
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 11, Pages 1835–1859
DOI: https://doi.org/10.1134/S0965542506110029
Bibliographic databases:
Document Type: Article
UDC: 519.653
Language: Russian
Citation: E. S. Zasukhina, “Fast automatic differentiation as applied to the computation of second derivatives of composite functions”, Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006), 1923–1949; Comput. Math. Math. Phys., 46:11 (2006), 1835–1859
Citation in format AMSBIB
\Bibitem{Zas06}
\by E.~S.~Zasukhina
\paper Fast automatic differentiation as applied to the computation of second derivatives of composite functions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 11
\pages 1923--1949
\mathnet{http://mi.mathnet.ru/zvmmf376}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2304067}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 11
\pages 1835--1859
\crossref{https://doi.org/10.1134/S0965542506110029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845329214}
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  • https://www.mathnet.ru/eng/zvmmf/v46/i11/p1923
  • This publication is cited in the following 1 articles:
    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
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    Full-text PDF :177
    References:45
    First page:1
     
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