CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
Development of algorithm of solutions of systems of linear equations with varied parameters using the matrix sparseness
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Read | Kochura Alexander Ye., Podkolzina Lyudmila V., Ivakin Yan A., Nidziev Ivan I. Development of algorithm of solutions of systems of linear equations with varied parameters using the matrix sparseness // Caspian journal : management and high technologies. — 2014. — №2. — pp. 101-115. |
Kochura Alexander Ye. - D.Sc. (Physics and Mathematics), Professor, St. Petersburg State Politechnical University, 34 Polytekhnicheskaya St., St. Petersburg, 195251, Russian Federation, kochura36@mail.ru
Podkolzina Lyudmila V. - Ph.D. (Pedagogics), Senior Lecturer, St. Petersburg State Politechnical University, 34 Polytekhnicheskaya St., St. Petersburg, 195251, Russian Federation, texnolog@zavod-vtuz.ru
Ivakin Yan A. - D.Sc. (Engineering), Leading Researcher, St. Petersburg Institute for Informatics and Automation of Russian Academy of Sciences, 39 14th line, Vasilyevsky Island, St. Petersburg, 199178, Russian Federation, ivakin@oogis.ru
Nidziev Ivan I. - Ph.D. (Engineering), Military Scientific Training Center of Navy of N.G. Kuznetsov Naval Academy, 18 Ushakovskaya nab., St. Petersburg, 197045, Russian Federation, ivan_005@mail.ru
The article describes a method for solving systems of linear equations with variable parameters, based on the use of sparse matrices calculated character processed , which is provided by the matrix equation purposeful structuring of the settlement system. The proposed method focuses primarily on large systems of linear equations with coefficient matrices densely filled. However, the transparent nature of the developed algorithms allows us to consider them useful and multivariate calculations of systems of linear equations of arbitrary dimension with different packing density matrices processed. Known methods of sparse matrix techniques generally based on different ways of converting the original randomly sparse matrix in a certain way to ensure an ordered structure of the original matrix. The proposed method does not impose any restrictions on the initial filling density matrix of coefficients of the settlement system. This matrix can be absolutely tight. Sparseness of the estimated matrix is provided by structuring it in the extended phase space. The main point of the proposed structuring is not filling in the realignment matrix having initially sparse nature and the equivalent transformation of the original matrix densely filled in sparse matrix with uniform structure required. When this information is used effectively solving the base system and provides a minimum profile of the sparsity of the estimated matrix with vector character variations of its coefficients. In particular, the simultaneous variation of all the coefficients of any row or column of the matrix of the original settlement structuring provides a minimum (one-dimensional) profile calculated matrix sparsity equivalent in the extended phase space.
Key words: systems of the linear equations, big dimension, multiple calculations, decomposition, technologies of the rarefied matrixes, the scheme of variations, диакоптика, the equation Krone, системы линейных алгебраических уравнений, большая размерность, многовар