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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2022 - 20232

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Ключові слова: search.filters.subject.multivariate polynomial regression

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  • Ескіз
    Документ
    Efficiency substantiation for a synthetical method of constructing a multivariate polynomial regression given by a redundant representation
    (Національний технічний університет "Харківський політехнічний інститут", 2023) Pavlov, Alexander Anatolievich; Holovchenko, Maxim Nikolaevich; Drozd, Valeriia Valeriivna
    In recent years, the authors in their publications have developed two different approaches to the construction of a multivariate polynomial (in particular, linear) regressions given by a redundant representation. The first approach allowed us to reduce estimation of coefficients for nonlinear terms of a multivariate polynomial regression to construction of a sequence of univariate polynomial regressions and solution of corresponding nondegenerate systems of linear equations. The second approach was implemented using an example of a multivariate linear regression given by a redundant representation and led to the creation of a method the authors called a modified group method of data handling (GMDH), as it is a modification of the well-known heuristic self-organization method of GMDH (the author of GMDH is an Academician of the National Academy of Sciences of Ukraine O. G. Ivakhnenko). The modification takes into account that giving a multivariate linear regression by redundant representation allows for construction of a set of partial representations, one of which has the structure of the desired regression, to use not a multilevel selection algorithm, but an efficient algorithm for splitting the coefficients of the multivariate linear regression into two classes. As in the classic GMDH, the solution is found using a test sequence of data. This method is easily extended to the case of a multivariate polynomial regression since the unknown coefficients appear in the multivariate polynomial regression in a linear way. Each of the two approaches has its advantages and disadvantages. The obvious next step is to combine both approaches into one. This has led to the creation of a synthetic method that implements the advantages of both approaches, partially compensating for their disadvantages. This paper presents the aggregated algorithmic structure of the synthetic method, the theoretical properties of partial cases and, as a result, the justification of its overall efficiency.
  • 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.