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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 8, Pages 1395–1400 (Mi zvmmf10437)  

This article is cited in 3 scientific papers (total in 3 papers)

Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner

R. R. Akhunov, T. R. Gazizov, S. P. Kuksenko

Tomsk State University of Control Systems and Radio Electronics, Tomsk, Russia

Abstract: The mean time needed to solve a series of systems of linear algebraic equations (SLAEs) as a function of the number of SLAEs is investigated. It is proved that this function has an extremum point. An algorithm for adaptively determining the time when the preconditioner matrix should be recalculated when a series of SLAEs is solved is developed. A numerical experiment with multiply solving a series of SLAEs using the proposed algorithm for computing 100 capacitance matrices with two different structures — microstrip when its thickness varies and a modal filter as the gap between the conductors varies — is carried out. The speedups turned out to be close to the optimal ones.

Key words: multiple solution of SLAEs, iterative method, preconditioning.

Funding Agency Grant Number
Russian Science Foundation 14-19-01232
Ministry of Education and Science of the Russian Federation 8.1802.2014/К
Russian Foundation for Basic Research 14-07-31267_мол_а

DOI: https://doi.org/10.7868/S0044466916080032

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:8, 1382–1387

Bibliographic databases:

UDC: 519.612
Received: 15.05.2015
Revised: 25.11.2015

Citation: R. R. Akhunov, T. R. Gazizov, S. P. Kuksenko, “Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner”, Zh. Vychisl. Mat. Mat. Fiz., 56:8 (2016), 1395–1400; Comput. Math. Math. Phys., 56:8 (2016), 1382–1387

Citation in format AMSBIB
\by R.~R.~Akhunov, T.~R.~Gazizov, S.~P.~Kuksenko
\paper Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 8
\pages 1395--1400
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 8
\pages 1382--1387

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    This publication is cited in the following articles:
    1. R. R. Gaynutdinov, S. F. Chermoshentsev, “Study of crosstalks in the cables of unmanned aerial vehicle”, 2017 International Siberian Conference on Control and Communications (SIBCON) Proceedings, IEEE, 2017  isi
    2. S. P. Kuksenko, R. R. Akhunov, T. R. Gazizov, “Choosing order of operations to accelerate strip structure analysis in parameter range”, International Conference Information Technologies in Business and Industry 2018, Journal of Physics Conference Series, 1015, IOP Publishing Ltd, 2018, 032076  crossref  isi  scopus
    3. Gazizov T.R., Sagiyeva I.Y., Kuksenko S.P., “Solving the Complexity Problem in the Electronics Production Process By Reducing the Sensitivity of Transmission Line Characteristics to Their Parameter Variations”, Complexity, 2019, 6301326  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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