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

Autor:	E. S. Zasukhina
Rok vydání:	2006
Předmět:	Hessian matrix Automatic differentiation Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Function (mathematics) System of linear equations Optimal control Computational Mathematics Runge–Kutta methods symbols.namesake symbols Gradient method Second derivative Mathematics
Zdroj:	Computational Mathematics and Mathematical Physics. 46:1835-1859
ISSN:	1555-6662 0965-5425
DOI:	10.1134/s0965542506110029
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b899c5d29f44847f4c058b1c647ee923 https://doi.org/10.1134/s0965542506110029 Zobrazit plný text záznamu Full text from SpringerLink