Automatska diferencijacija

U matematici i kompjuterskoj algebri, automatska diferencijacija (auto-diferencijacija, autodif ili AD), takođe nazvana algoritamska diferencijacija, računarska diferencijacija,^[1][2] je skup tehnika za procenu parcijalnog izvoda funkcije koju je odredio računarski program.

Automatsko diferenciranje koristi činjenicu da svaki računarski proračun, ma koliko bio komplikovan, izvršava niz elementarnih aritmetičkih operacija (sabiranje, oduzimanje, množenje, deljenje, itd.) i elementarnih funkcija (exp, log, sin, cos, itd.). Višekratnom primenom pravila lanca na ove operacije, delimični derivati proizvoljnog reda se mogu izračunati automatski, tačno sa radnom preciznošću i korišćenjem samo malog konstantnog faktora više aritmetičkih operacija originalnog programa.

Reference

1. Neidinger, Richard D. (2010). „Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming” (PDF). SIAM Review. 52 (3): 545—563. CiteSeerX 10.1.1.362.6580 . S2CID 17134969. doi:10.1137/080743627. 
2. Baydin, Atilim Gunes; Pearlmutter, Barak; Radul, Alexey Andreyevich; Siskind, Jeffrey (2018). „Automatic differentiation in machine learning: a survey”. Journal of Machine Learning Research. 18: 1—43. 

Literatura

• Rall, Louis B. (1981). Automatic Differentiation: Techniques and Applications. Lecture Notes in Computer Science. 120. Springer. ISBN 978-3-540-10861-0. 
• Griewank, Andreas; Walther, Andrea (2008). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Other Titles in Applied Mathematics. 105 (2nd изд.). SIAM. ISBN 978-0-89871-659-7. doi:10.1137/1.9780898717761. 
• Neidinger, Richard (2010). „Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming” (PDF). SIAM Review. 52 (3): 545—563. CiteSeerX 10.1.1.362.6580 . S2CID 17134969. doi:10.1137/080743627. Приступљено 2013-03-15. 
• Naumann, Uwe (2012). The Art of Differentiating Computer Programs. Software-Environments-tools. SIAM. ISBN 978-1-611972-06-1. 
• Henrard, Marc (2017). Algorithmic Differentiation in Finance Explained. Financial Engineering Explained. Palgrave Macmillan. ISBN 978-3-319-53978-2. 

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