Geodesic
On the peculiarities of the mathematical model of optimal dynamic measurement when implementing the spline method
Journal of computational and engineering mathematics, Tome 11 (2024) no. 1, pp. 24-33.

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The article presents the results of computational experiments demonstrating the importance of initial conditions in modeling the states of a measuring device in the algorithm of the spline method. The discussed algorithm is one of the numerical methods used in the theory of optimal dynamic measurements, which allow to find the input signal from a known output signal (or observation) and a known transfer function of the measuring device. In all formulations of the problem, it is assumed that the inertia of the measuring device is taken into account, and the differences are due to the inclusion of interferences of various natures in the mathematical model. Consideration of interference as “white noise” led to the development of analytical and numerical methods for solving the problem under discussion. The article briefly provides theoretical information and an overview of numerical methods for using digital filters to process observation results with subsequent application of the spline method. However, new experimental data have shown that the standard initial conditions are insufficient to ensure connectivity conditions in the internal nodes of the spline. The initial conditions are proposed in the article, and the results of computational experiments are presented.
Keywords: optimal dynamic measurements, spline method, Leontief type system, initial condition. 
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A. V. Keller; I. A. Kolesnikov. On the peculiarities of the mathematical model of optimal dynamic measurement when implementing the spline method. Journal of computational and engineering mathematics, Tome 11 (2024) no. 1, pp. 24-33. http://geodesic.mathdoc.fr/item/JCEM_2024_11_1_a3/