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Journal of Computer and Systems Sciences International
Erschienen in: Journal of Computer and Systems Sciences International 4/2019

01.07.2019 | COMPUTER METHODS

Synthesis of Fast and Superfast Solvers of Large Systems of Linear Algebraic Equations Using Control Theory Methods

verfasst von: M. G. Gadzhiev, K. V. Zhgun, N. E. Zubov, V. N. Ryabchenko

Erschienen in: Journal of Computer and Systems Sciences International | Ausgabe 4/2019

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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.
Vorheriger Artikel Method for Parametric Optimization in Problems of the Multichannel Control of Systems with Distributed Parameters
Nächster Artikel Large-Scale Problems with Quasi-Block Matrices

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Metadaten
Titel
Synthesis of Fast and Superfast Solvers of Large Systems of Linear Algebraic Equations Using Control Theory Methods
verfasst von
M. G. Gadzhiev
K. V. Zhgun
N. E. Zubov
V. N. Ryabchenko
Publikationsdatum
01.07.2019
Verlag
Pleiades Publishing
Erschienen in
Journal of Computer and Systems Sciences International / Ausgabe 4/2019
Print ISSN: 1064-2307
Elektronische ISSN: 1555-6530
DOI
https://doi.org/10.1134/S1064230719020084

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