Вісники НТУ "ХПІ"

Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/2494


З 1961 р. у ХПІ видається збірник наукових праць "Вісник Харківського політехнічного інституту".
Згідно до наказу ректора № 158-1 від 07.05.2001 року "Про упорядкування видання вісника НТУ "ХПІ", збірник був перейменований у Вісник Національного Технічного Університету "ХПІ".
Вісник Національного технічного університету "Харківський політехнічний інститут" включено до переліку спеціалізованих видань ВАК України і виходить по серіях, що відображають наукові напрямки діяльності вчених університету та потенційних здобувачів вчених ступенів та звань.
Зараз налічується 30 діючих тематичних редколегій. Вісник друкує статті як співробітників НТУ "ХПІ", так і статті авторів інших наукових закладів України та зарубіжжя, які представлені у даному розділі.

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2021 - 20222

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Ключові слова: search.filters.subject.normalized orthogonal polynomials of Forsythe

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Зараз показуємо 1 - 2 з 2
  • Ескіз
    Документ
    Construction of a multivariate polynomial given by a redundant description in stochastic and deterministic formulations using an active experiment
    (Національний технічний університет "Харківський політехнічний інститут", 2022) Pavlov, Alexander Anatolievich; Holovchenko, Maxim Nikolaevich; Drozd, Valeria Valerievna
    We present the methods for constructing a multivariate polynomial given by a redundant representation based on the results of a limited active experiment. We solve the problem in two formulations. The first is the problem of constructing a multivariate polynomial regression given by a redundant representation based on the results of a limited active experiment. The solution method is based on the previous results of Professor A. A. Pavlov and his students showing the fundamental possibility of reducing this problem to the sequential construction of univariate polynomial regressions and solving the corresponding nondegenerate systems of linear equations. There are two modifications of this method. The second modification is based on proving for an arbitrary limited active experiment the possibility of using only one set of normalized orthogonal polynomials of Forsythe. The second formulation refers to the solution of this problem for a particular but sufficient from the practical point of view case when an unknown implementation of a random variable is not added to the initial measurement results during an active experiment. This method is a modification of the solution method for the multivariate polynomial regression problem. Also, we used the main results of the general theory (which reduces the multivariate polynomial regression problem solving to the sequential construction of univariate polynomial regressions and solution of corresponding nondegenerate systems of linear equations) to consider and strictly substantiate fairly wide from the practical point of view particular cases leading to estimating the coefficients at nonlinear terms of the multivariate polynomial regression as a solution of linear equations with a single variable.
  • Ескіз
    Документ
    Estimating with a given accuracy of the coefficients at nonlinear terms of univariate polynomial regression using a small number of tests in an arbitrary limited active experiment
    (Національний технічний університет "Харківський політехнічний інститут", 2021) Pavlov, Alexander Anatolievich
    We substantiate the structure of the efficient numerical axis segment an active experiment on which allows finding estimates of the coefficients for nonlinear terms of univariate polynomial regression with high accuracy using normalized orthogonal Forsyth polynomials with a sufficiently small number of experiments. For the case when an active experiment can be executed on a numerical axis segment that does not satisfy these conditions, we substantiate the possibility of conducting a virtual active experiment on an efficient interval of the numerical axis. According to the results of the experiment, we find estimates for nonlinear terms of the univariate polynomial regression under research as a solution of a linear equalities system with an upper non-degenerate triangular matrix of constraints. Thus, to solve the problem of estimating the coefficients for nonlinear ter ms of univariate polynomial regression, it is necessary to choose an efficient interval of the numerical axis, set the minimum required number of values of the scalar variable which belong to this segment and guarantee a given value of the variance of estimates for nonlinear terms of univariate polynomial regression using normalized orthogonal polynomials of Forsythe. Next, it is necessary to find with sufficient accuracy all the coefficients of the normalized orthogonal polynomials of Forsythe for the given values of the scalar variable. The resulting set of normalized orthogonal polynomials of Forsythe al-lows us to estimate with a given accuracy the coefficients of nonlinear terms of univariate polynomial regression in an arbitrary limited active experiment: the range of the scalar variable values can be an arbitrary segment of the numerical axis. We propose to find an estimate of the constant and of the coefficient at the linear term of univariate polynomial regression by solving the linear univariate regression problem using ordinary least squares method in active experiment conditions. Author and his students shown in previous publications that the estimation of the coefficients for nonlinear terms of multivariate polynomial regression is reduced to the sequential construction of univariate regressions and the solution of the corresponding systems of linear equalities. Thus, the results of the paper qualitatively increase the efficiency of finding estimates of the coefficients for nonlinear terms of multivariate polynomial regression given by a redundant representation.