Synthesis of Fast and Superfast Solvers of Large Systems of Linear Algebraic Equations Using Control Theory Methods
- 作者: Gadzhiev M.1, Zhgun K.1, Zubov N.2, Ryabchenko V.1,2
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隶属关系:
- Moscow Power Engineering Institute (National Research University)
- Bauman State Technical University
- 期: 卷 58, 编号 4 (2019)
- 页面: 560-570
- 栏目: Computer Methods
- URL: https://journals.rcsi.science/1064-2307/article/view/220418
- DOI: https://doi.org/10.1134/S1064230719020084
- ID: 220418
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详细
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.
作者简介
M. Gadzhiev
Moscow Power Engineering Institute (National Research University)
Email: nik.zubov@gmail.com
俄罗斯联邦, Moscow
K. Zhgun
Moscow Power Engineering Institute (National Research University)
Email: nik.zubov@gmail.com
俄罗斯联邦, Moscow
N. Zubov
Bauman State Technical University
编辑信件的主要联系方式.
Email: nik.zubov@gmail.com
俄罗斯联邦, Moscow, 105005
V. Ryabchenko
Moscow Power Engineering Institute (National Research University); Bauman State Technical University
Email: nik.zubov@gmail.com
俄罗斯联邦, Moscow; Moscow, 105005
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