UDC 519.683.8:519.6 About Calculation Singularity of High-Order Derivative for Identification of the Graphic Objects Shape I. M. Gostev National Research University Higher School of Economics 20, Myasnitskaya str., Moscow, Russia, 101000 Methods 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. <...> 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. <...> Key words and phrases: graphic pattern recognition, image processing, computer geometry, calculation derivative, calculation accuracy, object identification, line correlation metrics. 1. <...> Introduction identification of curved lines which are fragments of some object contours. <...> Identification of the closed contours has been repeatedly stated in the literature, for example, in [1] and is based on the signature analysis and methods of geometrical correlation [2]. <...> Often in real conditions reception of the objects closed contours may be impossible; however it is easy to receive fragments of contours of object. <...> As numerical differentiation researches on calculation of derivative higher orders by various numerical methods have been conducted is in that case applied and the right accuracy from which it is necessary to calculate derivatives for identification of curves is defined. <...> The analysis of numerical methods of differentiation has shown the presence of a considerable quantity of various receptions. <...> A method of derivatives calculation on the basis of interpolation formulas. <...> Calculation of derivatives is carried out <...>