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

  • M. G. Gadzhiev
  • K. V. Zhgun
  • N. E. ZubovEmail author
  • V. N. Ryabchenko
COMPUTER METHODS

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.

Notes

ACKNOWLEDGMENTS

This work was supported by the Russian Science Foundation, project no. 19-19-00031.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • M. G. Gadzhiev
    • 1
  • K. V. Zhgun
    • 1
  • N. E. Zubov
    • 2
    Email author
  • V. N. Ryabchenko
    • 1
    • 2
  1. 1.Moscow Power Engineering Institute (National Research University)MoscowRussia
  2. 2.Bauman State Technical UniversityMoscowRussia

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