Yershov P. Intelligent system of computer mathematics for mathematical modeling in science and engineering

The dissertation is devoted to the development of principles, algorithmic support and software of an intelligent system of computer mathematics for automating the process of analysis and solving linear algebraic systems with sparse matrices on hybrid architecture computers. The introduction substantiates the relevance of the topic, formulates the purpose and tasks of the research, reveals the scientific novelty and practical value of the work, and presents its general characteristics. The first chapter is devoted to the review of the literature on the topic of the dissertation and justification of the choice of research direction. The second chapter explores the mathematical apparatus of computer research of linear systems with approximate data; a parallel block algorithm for LLT-factorization of "cloud" matrix was developed, the acceleration and efficiency of parallel algorithms were investigated. In the third chapter, algorithms for automatic identification of the structure of sparse matrices and their regularization based on machine learning methods and neural network technologies are developed. A convolutional neural network "Sparse Matrix Vision" was built. Software implementation and numerical experiments were carried out. In the fourth chapter, principles, architecture, and composition of the intelligent system of computer mathematics (ISCM) for automating the process of research and problem solving are developed, and its computer implementation is proposed. The results of practical computations are presented. The effectiveness of algorithmic and software of ISCM on a number of problems of mathematical modeling in the construction industry was studied.