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Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals
Computer Research and Modeling, 2014, v. 6, no. 2, pp. 189-202The problem of restoration of an element f of Euclidean functional space L2(X) based on the results of measurements of a finite set of its linear functionals, distorted by (random) error is solved. A priori data aren't assumed. Family of linear subspaces of the maximum (effective) dimension for which the projections of element f to them allow estimates with a given accuracy, is received. The effective rank ρ(δ) of the estimation problem is defined as the function equal to the maximum dimension of an orthogonal component Pf of the element f which can be estimated with a error, which is not surpassed the value δ. The example of restoration of a spectrum of radiation based on a finite set of experimental data is given.
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Motion control simulating in a viscous liquid of a body with variable geometry of weights
Computer Research and Modeling, 2011, v. 3, no. 4, pp. 371-381Views (last year): 2. Citations: 16 (RSCI).Statement of a problem of management of movement of a body in a viscous liquid is given. Movement bodies it is induced by moving of internal material points. On a basis the numerical decision of the equations of movement of a body and the hydrodynamic equations approximating dependencies for viscous forces are received. With application approximations the problem of optimum control of body movement dares on the set trajectory with application of hybrid genetic algorithm. Possibility of the directed movement of a body under action is established back and forth motion of an internal point. Optimum control movement direction it is carried out by motion of other internal point on circular trajectory with variable speed.
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International Interdisciplinary Conference "Mathematics. Computing. Education"