Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8387Research ArticleAbout Calculation Singularity of High-Order Derivative for Identification of the Graphic Objects ShapeGostevI Migostev@gmail.comNational Research University Higher School of Economics15022014233133508092016Copyright © 2014,2014Methods of calculation of high order derivatives are considered on a basis: interpolation formulas; “without difference methods of calculation of derivatives”; applications of convolution with replacement of differentiation by integration operation; differentiation with use of quadratures on C. Lanczos; the method of Numerova. The comparative analysis of methods of calculation of high order derivatives on accuracy of calculations with use as the sample of the derivatives calculated in package Maple with 20 digit decimal accuracy is carried out. It is shown that all methods are almost equivalent on accuracy and are reduced to convolution calculation between differentiated function and some window which coefficient depend on an applied method. For carrying out of experiments the special program complex is developed for calculation of high order derivative (up to 7th) the tabulated functions with various step. Grids with steps from 0.005 to 0.1 have been investigated. Irrespective of a method of calculation of derivatives it has been defined that optimum value of step mesh for 64 digit arithmetic’s the step is from 0.01 till 0.05. Value of smooth functions differs less than their accuracy of representation at smaller value of a step, and at greater step - the differentiation error increases. Results of experiments confirm N.N. Kalitkin’s theoretical conclusions.graphic pattern recognitionimage processingcomputer geometrycalculation derivativecalculation accuracyobject identificationline correlation metricsраспознавания графических образовобработка изображенийкомпьютерная геометриявычисление производныхточность вычисленийидентификация объектовметрики линейной корреляции[Gonzales R. C., Woods R. E. Digital Image Processing (2nd Edition). - New Jersey: Prentice-Hall, Inc., 2002.][Gostev I. M. On Recognition Methods for Graphical Patterns // Journal of Computer and Systems Sciences International. - 2004. - No 1. - Pp. 138-144.][Gostev I. M. On the Identification of Unclosed Curves // Pattern Recognition and Image Analysis. - 2013. - Vol. 23, No 2. - Pp. 217-225.][Березин И. С., Жидков Н. П. Методы вычислений. Том 1. - М.: Физматлит, 1962.][Abramowitz M., Stegun I. Handbook of Mathematical Functions. - Washington: U.S National Bureau of Standards, 1964.][Гельфанд И. М., Шилов Г. Е. Обобщённые функции. - М.: Физматлит, 1959.][Lanczos C. Applied Analysis. - New Jersey: Prentice Hall, Inc., 1956.][Калиткин Н.Н. Численные методы. - М.: Наука, 1978.]