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Том 42, № 2 (2018)
- Год: 2018
- Статей: 7
- URL: https://journals.rcsi.science/0278-6419/issue/view/10808
Article
Numerical Solution of a Semilinear Matrix Equation of the Stein Type in the Normal Case
Аннотация
It is known that the solution of the semilinear matrix equation X − AX*B = C can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. A technique for solving the original semilinear equation in the normal case is proposed. For equations of the order n = 3000, this allows us to cut the time of computation almost in half, compared toMatlab’s library function dlyap, which solves Stein equations in the Matlab package.
51-54
An Iterative Way of Solving the Inverse Scattering Problem for an Acoustic System of Equations in an Absorptive Layered Nonhomogeneous Medium
Аннотация
An algorithm is considered for solving the inverse scattering problem of seismic waves in a layered medium. The algorithm is based on solving a nonclassical ordinary differential equation with respect to an acoustic impedance, which also contains an unknown function characterizing the dissipative properties of the medium. The uniqueness of determining of these functions and the functional dependence associating them is established by solving the inverse problem of ground seismics. Results are presented from a computing experiment on applying the proposed algorithm.
55-62
A New Algorithm for Generating Tetrahedral Grids
Аннотация
A new algorithm is presented for generating tetrahedral grids for bound domains of complicated structure and form that consist of the union of several subdomains. The grids obtained using the algorithm have regularity, in that there is no tetrahedron whose vertices lie at different sides of the subdomain boundaries. The algorithm has high fast-action: the time needed to generate a grid consisting of 105−106 tetrahedrons is approximately 20–40 seconds of the work of a standard personal computer. All steps of the algorithm are described in detail, and examples of generated grids are given.
63-68
Algorithm for Constructing a Guaranteeing Program Package in a Control Problem with Incomplete Information
Аннотация
A package control problem is considered for a target set at a moment of time. The dynamic system under control is described by linear differential equations, the control area is a convex compact, and the target set is convex and closed. A version of the subsequent approximations method in extended space is proposed for constructing elements of a guaranteeing program package in the case of regular clusters.
69-79
A Coordinate-Wise Estimate of the Reachability Set of a Controlled System
Аннотация
The problem of a coordinate-wise estimate of the reachability set for nonlinear controlled systems is considered. Estimates of this kind are useful because they allow us at least in rough form to assess the dynamic possibilities of a controlled system.
80-84
Limit Theorems for Risk Estimate in Models with Non-Gaussian Noise
Аннотация
The problem of constructing an estimate of a signal function from noisy observations, assuming that this function is uniformly Lipschitz regular, is considered. The thresholding of empirical wavelet coefficients is used to reduce the noise. As a rule, it is assumed that the noise distribution is Gaussian and the optimal parameters of thresholding are known for various classes of signal functions. In this paper a model of additive noise whose distribution belongs to a fairly wide class, is considered. The mean-square risk estimate of thresholding is analyzed. It is shown that under certain conditions, this estimate is strongly consistent and asymptotically normal.
85-88
Optimal Positioning of Service Stations
Аннотация
An effective new algorithm is presented for positioning service stations for calls which come from a subset of the line. The coordinate of a call is a random quantity which has a distribution density with compact support. The asymptotic second order optimality of this algorithm is found. A necessary optimality condition of positioning stations for a family of optimality criteria is also found.
89-96