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Hartman, Jan; Lukšan, Ladislav; Zítko, Jan

Automatic differentiation and its program realization. (English) Zbl 1191.65017

Kybernetika 45, No. 5, 865-883 (2009).
Automatic differentiation is an efficient method for evaluating derivatives of functions given by computer programs, see A. Griewank and A. Walther [Evaluating derivatives. Principles and techniques of algorithmic differentiation. 2nd ed. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). (2008; Zbl 1159.65026)]. In this paper, the authors discuss some properties of automatic differentiation and describe algorithms for computing of derivatives in the forward and reverse mode. The corresponding implementation is prepared in the interactive system UFO (= Universal Functional Optimization) developed in the Institute of Computer Science of the Academy of Sciences of the Czech Republic.
Reviewer: Manfred Tasche (Rostock)

MSC:

65D25 Numerical differentiation
68W30 Symbolic computation and algebraic computation
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems

Keywords:

automatic differentiation; functions given by computer programs; algorithmic differentiation; program realization; modeling language; universal functional optimization

Citations:

Zbl 1159.65026

Software:

ADOL-C; UFO
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\textit{J. Hartman} et al., Kybernetika 45, No. 5, 865--883 (2009; Zbl 1191.65017)
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References:

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[2] Automatic Differentiation: Applications, Theory, and Implementations. Springer-Verlag, Berlin 2005. · Zbl 1084.65002
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[8] J. Hartman and L. Lukšan: Automatické derivování v systému UFO (Automatic Differentiation in System UFO). Technical Report V-1002. ICS AS CR, Prague 2007.
[9] J. Hartman and J. Zítko: Principy automatického derivování (Principles of Automatic Differentiation). Technical Report, Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Prague 2006.
[10] L. Lukšan, M. Tůma, J. Hartman, J. Vlček, N. Ramešová, M. Šiška, and C. Matonoha: UFO 2006 - Interactive System for Universal Functional Optimization. Technical Report V-977. ICS AS CR, Prague 2006.
[11] A. Verma: Structured Automatic Differentiation. Ph.D. Thesis, Cornell University, 1988.
[12] A. Walther, A. Griewank, and O. Vogel: ADOL-C: Automatic differentiation using operator overloading in C++. PAMM 2 (2003), 41-44. · Zbl 1201.68161
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.