Article

Article title THE ALGORITHM FOR OPTIMIZATION OF DISCRETE APPROXIMATIONS OF TABULATED FUNCTIONS
Authors V. A. Antonov
Section SECTION III. MODELING OF COMPLEX SYSTEMS
Month, Year 07, 2017 @en
Index UDC 519.863
DOI
Abstract The algorithm of nonlinear and multidimensional optimization of functions used in discrete approximation of complex tabulated dependencies from a sample of node-points is considered. The formulation of a mathematical problem reduced to the search for coefficients and functional pa-rameters of the approximating model that provide the largest coefficient of its determination is given. The algorithm, in connection with the limited possibilities of known optimization methods, is constructed from a simplified version of the alternative method of approximations of a parabolic vertex. It is shown that this algorithm leads to a stable convergence of the computation of the pa-rameters of the unimodal functions identified in the models. As a result of successive alternation of such functions, the desired set of optimal parameters of the model is determined. As part of the practical implementation of the above algorithm, approximations of the Laplace integral functions and quantiles x2 of the Pearson distribution are considered. The general form of the approximat-ing models consists of different functions, including a quasi-step function, an amplitude-damped sine, and polynomials of power functions. Basing on the optimization results determined are the coefficients and from three to seven functional parameters contained in the models. It is shown that the Laplace function is approximated with a coefficient of determination of 0,99998 and a standard deviation of 0,00063 in the nodal points, permissible for engineering estimates. In the approximation of the x2 distribution, a high determination coefficient of 0,9998 is also used. It is noted that the simplicity and compactness of the approximation models makes it possible to apply them in automation and control systems for performing statistical calculations of the reliable func-tioning of technological processes.

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Keywords Function; nonlinear optimization; algorithm; iteration; discrete approximation.
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