DEVELOPMENT OF AN AGENT-BASED ALGORITHM FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS OF LARGE DIMENSION
Abstract
Solving systems of linear algebraic equations (SLAE) is one of the most important fundamental tasks in the development of a new generation of design systems in various fields of science and technology. The relevance of this study is due to the growing volume of data and the increasing complexity of tasks. Traditional methods for solving of SLAE, such as the Gauss method, the run-through method, iterative methods (Jacobi method, Seidel method, etc.), have proven themselves well when working with relatively small systems. However, when solving large-dimensional of SLAE, these methods are not efficient enough due to high computational costs and memory requirements. One of the promising approaches to solving problems of high complexity is the use of agent-based systems. Agent-based systems offer a new way of organizing computing processes based on the interaction of independent agents, each of whom performs a specific part of the task. This approach allows for more flexible allocation of computing resources and efficient solution of complex tasks in a big data environment. A method for solving equations describing a mathematical model of a circuit is presented, taking into account the optimization of the ratio between the accuracy of calculations and the time of their execution. In this paper, we propose an agent-based algorithm for solving systems of linear algebraic equations of large dimension. During the development of this algorithm, an analysis of existing methods and algorithms for solving of SLAE was carried out, their advantages and disadvantages were identified. An agent-oriented architecture was developed to solve large-scale of SLAE, the organization of agent interaction and mechanisms for distributing tasks between them were proposed. A software implementation of the developed algorithm was performed. To evaluate the effectiveness of the proposed approach, it was tested on a number of test tasks. The performance and scalability of the developed algorithm were also evaluated, and it was compared with traditional methods for solving of SLAE.
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