scholarly journals ANALYSIS OF CALCULATION METHODS, OBTAINING ESTIMATES AND ENSURING THE ACCURACY OF SIMULATION OF CONTROL OBJECTS

InterConf ◽  
2021 ◽  
pp. 485-499
Author(s):  
Daria Lys
Keyword(s):  
Nonlinear Systems ◽  
Sensitivity Function ◽  
Distribution Functions ◽  
A Posteriori ◽  
Algebraic Equations ◽  
Mathematical Apparatus ◽  
Practical Application ◽  
Calculation Methods ◽  
Linear Algebraic Equations ◽  
A Posteriori Estimates

Systems of linear algebraic equations are a mathematical apparatus that is widely used in solving a significant number of problems in the practical application of mathematics and engineering. The analysis of errors in solving linear algebraic equations and the sensitivity function of nonlinear systems using the method of equivalent excitations, which, in turn, makes it possible to make informed decisions on the choice and development of methods for studying the accuracy of computing devices. Methods for constructing estimates «from below» of the distribution functions of the fatal error of the numerical solution of systems of linear algebraic equations are also presented, in particular, a posteriori estimates of the effectiveness of the methods under study are analyzed.

Testing the systems with fuzzy discrete components

2020 ◽  
Vol 6 (4) ◽  
pp. 518-531
Author(s):  
D. V. Speransky ◽  
◽  
A. V. Gorelik ◽  
I. A. Zhuravlev ◽  
A. V. Orlov ◽  
...  
Keyword(s):  
Intelligent Systems ◽  
Synthesis Method ◽  
Analytical Models ◽  
Synthesis Methods ◽  
Algebraic Equations ◽  
Mathematical Apparatus ◽  
Hybrid Intelligent Systems ◽  
Test Synthesis ◽  
Linear Algebraic Equations ◽  
Fuzzy Objects

Modern complex systems are build based on heterogeneous components with various interrela tionships, fuzziness, and uncertainty of the laws of functioning of the components and the system. An important class of such systems comprises hybrid intelligent systems, where the components are represented by analytical models of fuzzy objects, artifi cial neural networks, expert systems, etc. The article considers fuzzy discrete devices being, for example, part of hybrid systems. Fuzzy linear automata (FLA) introduced in the article are used as a mathematical model of such components. The problem of test synthesis for FLA used to detect faults in them is discussed. Normal single-stuck faults are permissible faults in FLA. The faults originating from the replacement of some elements of the FLA characteristic matrices with others (from a given set of alternative ones) are also permissible. Test synthesis methods for FLA belonging to the class of m-deterministic and synchronized automata, as well as arbitrary linear automata have been developed. The fi rst two methods are based on reducing the considered problem of solving systems of linear algebraic equations. It should be noted that there is a well-developed mathematical apparatus applying a few eff ective methods for searching for such solutions. The tests synthesized by these methods for m-deterministic and synchronized FLA are sufficiently short and do not exceed the memory depth of the corresponding automata. It is shown that the conditions for an FLA referring to the two fi rst classes mentioned above are not too strict. It is noted that the known methods of test synthesis for linear automata require compliance with much more stringent requirements. The synthesis method for arbitrary FLA also builds short tests

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova
Keyword(s):  
Effective Conductivity ◽  
Dimensional Space ◽  
Elementary Function ◽  
Voronoi Tessellation ◽  
Random Packing ◽  
Periodicity Cell ◽  
Algebraic Equations ◽  
Optimal Packing ◽  
Linear Algebraic Equations ◽  
Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

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