Synthesis of Fast and Superfast Solvers of Large Systems of Linear Algebraic Equations Using Control Theory Methods
| Autor: | N. E. Zubov, V. N. Ryabchenko, Ksenia Zhgun, Magomed Gadzhiev |
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| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Computer Networks and Communications Computer science Applied Mathematics 010102 general mathematics Zero (complex analysis) 02 engineering and technology Mechatronics 01 natural sciences Theoretical Computer Science Algebraic equation 020901 industrial engineering & automation Exact solutions in general relativity Control and Systems Engineering Control theory ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Decomposition (computer science) Applied mathematics Computer Vision and Pattern Recognition 0101 mathematics Software Linear equation Information Systems |
| Zdroj: | Journal of Computer and Systems Sciences International. 58:560-570 |
| ISSN: | 1555-6530 1064-2307 |
| Popis: | Algorithms for fast and superfast solvers of large systems of linear algebraic equations are proposed. These algorithms are constructed based on a novel method of multistep decomposition of a multidimensional linear dynamic system. Examples of the analytical synthesis of iterative solvers for matrices of the general form and for large numerical systems of linear algebraic equations are presented. Analytical calculations show that the exact solution in iterative processes with zero initial conditions is obtained already at the second iteration step. Investigation of the synthesized solvers of large linear equations with numerical matrices and vectors the elements of which are normally distributed showed that the iterative processes converge at the third or fourth iteration step to a highly accurate solution independently of the problem size. |
| Databáze: | OpenAIRE |
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