Geodesic
Automatic differentiation and its program realization
Kybernetika, Tome 45 (2009) no. 5, pp. 865-883.

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Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its principles can be applied in other systems. We describe, how the operations are stored in the first part of the derivative computation and how the obtained records are effectively used in the second part of the computation.
Classification : 26A24, 65D25, 65K99, 68W30
Keywords: automatic differentiation; modeling languages; systems for optimization 
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     author = {Hartman, Jan and Luk\v{s}an, Ladislav and Z{\'\i}tko, Jan},
     title = {Automatic differentiation and its program realization},
     journal = {Kybernetika},
     pages = {865--883},
     publisher = {mathdoc},
     volume = {45},
     number = {5},
     year = {2009},
     mrnumber = {2599117},
     zbl = {1191.65017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_5_a11/}
}
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Hartman, Jan; Lukšan, Ladislav; Zítko, Jan. Automatic differentiation and its program realization. Kybernetika, Tome 45 (2009) no. 5, pp. 865-883. http://geodesic.mathdoc.fr/item/KYB_2009__45_5_a11/