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Optimal Factorization of Operators by Operators That Are Consistent with the Graph’s Structure

  • Victoria Goncharenko
  • Yuri Goncharenko
  • Sergey Lyashko
  • Vladimir Semenov
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 139)

Abstract

In this paper we introduce the notion of an operator that is consistent with the structure of a graph and the computational system that is universal in the class of operators. The model fully corresponds to the processes occurring in distributed computing systems. The problem of the factorization of operators by operators consistent with the structure of a graph is formulated. We prove the criterion for the factorization of a linear invertible operator acting in a finite-dimensional linear space. We obtain upper estimations of the factorization depth of the class of linear invertible operators by linear operators compatible with the structure of the graph.

Notes

Acknowledgements

This research is supported by the Ministry of Education and Science of Ukraine (project 0116U004777). Vladimir Semenov thanks the State Fund for Fundamental Researches of Ukraine for support.

References

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    V. Yu. Goncharenko, Some properties of operators that are consistent with the graph structure, in Operations Research and ACS, vol. 23, (KSU, Kiev, 1984), pp. 73–81Google Scholar
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    V. Yu. Goncharenko, B.B. Nesterenko, Asynchronous principles in parallel computing, part II. WP of Institute of Mathematics of the NASU, no. 82–38. Kiev, 1982Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Victoria Goncharenko
    • 1
  • Yuri Goncharenko
    • 1
  • Sergey Lyashko
    • 1
  • Vladimir Semenov
    • 1
  1. 1.Department of Computational MathematicsTaras Shevchenko Kiev National UniversityKievUkraine

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