Результаты поиска по 'generalized matrix Riccati equations':
Найдено статей: 2
  1. Chujko S.M., Nesmelova (Starkova) O.V., Sysoev D.V.
    Nonlinear boudary value problem in the case of parametric resonance
    Computer Research and Modeling, 2015, v. 7, no. 4, pp. 821-833

    We construct necessary and sufficient conditions for the existence of solution of seminonlinear matrix boundary value problem for a parametric excitation system of ordinary differential equations. The convergent iteration algorithms for the construction of the solutions of the semi-nonlinear matrix boundary value problem for a parametric excitation system differential equations in the critical case have been found. Using the convergent iteration algorithms we expand solution of seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation in the neighborhood of the generating solution. Estimates for the value of residual of the solutions of the seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation are found.

    Keywords: seminonlinear boundary value problem, matrix differential equations, generalized Green’s operator, parametric excitation.
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  2. Varshavsky L.E.
    Studying indicators of development of oligopolistic markets on the basis of operational calculus
    Computer Research and Modeling, 2019, v. 11, no. 5, pp. 949-963

    The traditional approach to computing optimal game strategies of firms on oligopolistic markets and of indicators of such markets consists in studying linear dynamical games with quadratic criteria and solving generalized matrix Riccati equations.

    The other approach proposed by the author is based on methods of operational calculus (in particular, Z-transform). This approach makes it possible to achieve economic meaningful decisions under wider field of parameter values. It characterizes by simplicity of computations and by necessary for economic analysis visibility. One of its advantages is that in many cases important for economic practice, it, in contrast to the traditional approach, provides the ability to make calculations using widespread spreadsheets, which allows to study the prospects for the development of oligopolistic markets to a wide range of professionals and consumers.

    The article deals with the practical aspects of determining the optimal Nash–Cournot strategies of participants in oligopolistic markets on the basis of operational calculus, in particular the technique of computing the optimal Nash–Cournot strategies in Excel. As an illustration of the opportinities of the proposed methods of calculation, examples close to the practical problems of forecasting indicators of the markets of high-tech products are studied.

    The results of calculations obtained by the author for numerous examples and real economic systems, both using the obtained relations on the basis of spreadsheets and using extended Riccati equations, are very close. In most of the considered practical problems, the deviation of the indicators calculated in accordance with the two approaches, as a rule, does not exceed 1.5–2%. The highest value of relative deviations (up to 3–5%) is observed at the beginning of the forecasting period. In typical cases, the period of relatively noticeable deviations is 3–5 moments of time. After the transition period, there is almost complete agreement of the values of the required indicators using both approaches.

    Keywords: oligopolistic markets, operational calculus, generalized matrix Riccati equations, spreadsheets, factorization.

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