Solution of the Block System with Numerical Elements in the Matlab Environment

• Дата: 2019
• Автори: Семчишин, Ліда Михайлівна, Павелчак-Данилюк, Ольга Богданівна
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Кам'янець-Подільський національний університет імені Івана Огієнка 2019
• Онлайн доступ: http://mcm-math.kpnu.edu.ua/article/view/188987
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

The new approach to a block system of linear algebraic equations with numerical elements is proposed.  A method of unblocking systems with some of the most common ways of filling is considered. We find the solution of the system as the relation of two polynomials, and the unknowns are calculated by the method of uncertain coefficients.  By grouping the members at equal degrees and determining unknown coefficients, a system was used to solve them using a cutting scheme algorithm.  For this purpose the system matrix is divided into blocks.  Unbundling the resulting systems required some intermediate matrix operations.  Thus, with the full implementation of the cutting circuit algorithm for the system, a number of arithmetic operations were performed.  High accuracy of the proposed method of resolution is shown.ESSELS has been written and tested to solve a block system of linear algebraic equations with numerical elements in MatLab.  This function implements the algorithm for solving systems of linear algebraic equations by the method of truncated systems. This algorithm allows to solve systems of equations in the case of symmetric filling (the number of sub-diagonals is equal to the number of diagonals) and when the number of sub-diagonals and super-diagonals of the matrix is different. A small program is written for comparison with regular MatLab linear algebra programs. It implements the procedure of solving a block system of linear algebraic equations with numerical elements by means of MatLab.  The comparison results in the table are given.  The proposed algorithms for this medium-sized test system have significant advantages over standard MatLab features.  The algorithm for solving a system of linear algebraic equations with numerical elements in the MatLab environment is tested. The efficiency of the proposed algorithm is shown in the paper.  The theoretical and methodological basis of the study are the methods of optimization and mathematical modeling.The proposed algorithm can be effectively used in computer algebra systems and for analytical and numerical solution of engineering and applied problems.