Geodesic
Calculation of the derivative of an inaccurately defined function by means of feedback laws
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 231-243

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The problem of calculating the derivative of an inaccurately defined function is considered. This problem is one of the “classical” problems in mathematical analysis. Various algorithms for solving this problem have been proposed by many authors. In the present study, constructions of positional control theory are invoked to solve this problem. Due to the presence of error in the measurement of the values of a function, the exact calculation of the derivative seems to be impossible. In view of this feature, a problem solving algorithm is presented that is based on an appropriate modification of the method of models controlled by feedback laws and is robust with respect to informational noise and measurement errors. 
@article{TRSPY_2015_291_a16,
     author = {V. I. Maksimov},
     title = {Calculation of the derivative of an inaccurately defined function by means of feedback laws},
     journal = {Informatics and Automation},
     pages = {231--243},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a16/}
}
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V. I. Maksimov. Calculation of the derivative of an inaccurately defined function by means of feedback laws. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 231-243. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a16/