Synthesis of Fast and Superfast Solvers of Large Systems of Linear Algebraic Equations Using Control Theory Methods
- Authors: Gadzhiev M.G.1, Zhgun K.V.1, Zubov N.E.2, Ryabchenko V.N.1,2
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Affiliations:
- Moscow Power Engineering Institute (National Research University)
- Bauman State Technical University
- Issue: Vol 58, No 4 (2019)
- Pages: 560-570
- Section: Computer Methods
- URL: https://journals.rcsi.science/1064-2307/article/view/220418
- DOI: https://doi.org/10.1134/S1064230719020084
- ID: 220418
Cite item
Abstract
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.
About the authors
M. G. Gadzhiev
Moscow Power Engineering Institute (National Research University)
Email: nik.zubov@gmail.com
Russian Federation, Moscow
K. V. Zhgun
Moscow Power Engineering Institute (National Research University)
Email: nik.zubov@gmail.com
Russian Federation, Moscow
N. E. Zubov
Bauman State Technical University
Author for correspondence.
Email: nik.zubov@gmail.com
Russian Federation, Moscow, 105005
V. N. Ryabchenko
Moscow Power Engineering Institute (National Research University); Bauman State Technical University
Email: nik.zubov@gmail.com
Russian Federation, Moscow; Moscow, 105005