NUMERICAL METHOD OF THE SOLUTION OF THE TENSOR EQUATIONS KRON FOR TWO-LEVEL HIERARCHICAL SYSTEM

UDC 519.676

D.E. Orlova

The numerical method of the solution of the tensor equations Kron for two-level hierarchical system in the presence of relevant communications of mutual influence between its components is considered. The idea of a method consists that the detailed account of communications of interference, actually and causing difficulties of the decision of the given equations, is substituted for typical algorithms of optimization of coordination type. The choice of type of algorithm is anticipated a quantitative estimation of degree of a mismatch of parameters of the components, the system theory of the conflict based on ideas. It is shown that all variety of mismatches can be reduced to three typical variants: to an essential mismatch, practical absence of local mismatches and an insignificant mismatch on minor questions. In the first variant for normal functioning of system it is required, that in it system interests dominated. In the second variant the decision of problems can be given on level of components of system. In the third variant to eliminate mismatches it is possible on the basis of parity of system and local interests. Algorithms of optimization corresponding to these variants are described: at domination of system interests, at domination of local interests and at parity of interests. The method is realized in the form of a program complex on the basis of Visual Basic programming systems, S ++ and Delphi. Numerical experiment proves convergence of algorithms of optimization. The method can find practical application as the tool of support of decision-making at management difficult dynamic system of hierarchical type.

Keywords: :tensor equations Kron, numerical method, optimization, mismatch, program complex, algorithm, convergence.

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