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Chapter
Interflatation of Functions
This chapter presents the operators of interflatation of functions of three variables on a system of mutually perpendicular planes using rational, polynomial, trigonometric auxiliary functions, and auxiliary f...
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Chapter
Testing the Quality of Algorithm Programs
This chapter outlines both the theoretical foundations of testing algorithms and programs, and practical (programs differ from algorithms by the presence of rounding errors). In particular, the subject and pur...
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Chapter
Elements of the Computing Theory
This chapter is devoted to the further development of the theory of computational errors, namely, the work proposes a combined approach to assessing the quality of the solution of the problem. This takes into ...
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Chapter
Interlineation of Functions
This chapter is devoted to the construction and study of interlineation operators of functions of two or more variables with and without preservation of the class of differentiation. When constructing interlin...
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Chapter
Cubature Formulae Using Interlineation of Functions
This chapter presents the cubature formulas for calculating the integrals of the functions of two variables, which are obtained by replacing the subintegral function by spline interlineation operators. The cub...
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Chapter
Computer Technologies of Solving Problems of Computational and Applied Mathematics with Fixed Values of Quality Characteristics
This chapter describes computer technologies for solving problems of computational and applied mathematics with given values of quality characteristics in accuracy and speed. This technology is suitable for an...
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Book
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Chapter
Theories of Computational Complexity
This chapter is devoted to the issues of algebraic and analytical computational complexity of problem solving. The main focus is on computer technology for computational processes, which is covered for various...
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Book
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Book
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Chapter
Supercomputers and Intelligent Technologies in High-Performance Computations
Early 1980s saw the beginning of the development of the new architecture of multiprocessor supercomputers. At the same time, macro-pipeline computing system was developed in Ukraine. The industrial samples of ...
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Chapter
Theoretical and Applied Programming
The chapter presents the main results of the automatic–algebraic approach proposed by Glushkov and his followers in theoretical and applied programming, which laid the foundation of the Kyiv School of Cybernet...
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Chapter
Information Technologies as Tools for Studying Complex Processes
The chapter refers to the development of high-performance supercomputer systems, reconfigurable knowledge-oriented computer systems, problem-oriented systems for digital signal processing, computer instrumenta...
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Chapter
Mathematical Modeling and Analysis of Complex Processes
The chapter addresses some aspects of modern computational mathematics concerning the mathematical modeling of processes in multicomponent media, wave processes in homogeneous and inhomogeneous infinite wavegu...
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Chapter
Combinatorial Optimization Problems
We consider combinatorial optimization problems (COP), i.e., finding extrema of an objective function on a combinatorial space. Many various important applied and theoretical problems of different degree of co...
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Chapter
Modeling of Structural, Institutional and Technological Changes
Financial crisis in the form of malfunction in money turnover had become one of the first serious problems faced by the post-communist countries in their transition from centralized planned economy to an open-...
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Chapter
Modeling of Foreign Economic Activity in a Transition Economy
Practically all the former socialist countries started their market reforms under the conditions of isolation from the world markets, out of the international system of labor division, which existed then in th...
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Chapter
Mathematical Modeling and Information Technologies for the Analysis of Economic Processes
We consider information technologies that include the following interindustry aggregated balance models to identify the main lines of structural and technological changes: economic dynamics given imperfect com...
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Chapter
Optimization Methods for Solving Problems of Transcomputational Complexity
This chapter addresses subgradient nonsmooth optimization methods. The generalized gradient descent method known later as the subgradient method is considered. It was used to solve many high-dimensional proble...
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Chapter
Computer Technologies in Medical and Biological Research
The chapter highlights interesting results obtained in decoding the genetic information for models of DNA, proteins, and important processes in cells of the human body. The symmetry rules are established, and ...