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Adaptive Computer Technologies for Solving Problems of Computational and Applied Mathematics

  • SOFTWARE–HARDWARE SYSTEMS
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Cybernetics and Systems Analysis Aims and scope

Abstract

A technology is proposed for automated solving of problems with innovative capabilities on the class of problems that is a system of linear algebraic equations. The application efficiency of computer technologies is considered from the point of view of implementing the three following basic paradigms of computer modeling: computer mathematics, high performance computing (HPC), and intelligent interface. The implementation of these factors as compared to traditional technologies allows for substantial redistribution of works in the process of problem statement and solution between the user and the computer, reducing the terms of development of applications for solving scientific and technical problems, and increase of the computer solution accuracy.

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References

  1. Top 500, June (2021). URL: https://top500.org/statistics/list/.

  2. I. N. Molchanov (ed.), Numerical Methods for a Multiprocessor Computer ES Complex [in Russian], VVIA im. prof. N. Ye. Zhukovskogo, Moscow (1986).

    Google Scholar 

  3. A. N. Khimich, I. N. Molchanov, A. V. Popov, T. V. Chistyakova, and M. F. Yakovlev, Parallel Algorithms to Solve Problems in Computational Mathematics [in Russian], Naukova Dumka, Kyiv (2008).

    Google Scholar 

  4. I. V. Sergienko, I. N. Molchanov, and A. N. Khimich, “Intelligent technologies of high-performance computing,” Cybern. Syst Analysis, Vol. 46, No. 5, 833–844 (2010). https://doi.org/10.1007/s10559-010-9265-3.

    Article  Google Scholar 

  5. A. N. Khimich, A. V. Popov, and V. V. Polyanko, “Algorithms of parallel computations for linear algebra problems with irregularly structured matrices,” Cybern. Syst. Analysis, Vol. 47, No. 6, 973–985 (2011). 0.1007/s10559-011-9377-4.

  6. O. M. Khimich and A. Y. Baranov, “Hybrid algorithm for solving linear systems with tape matrix direct methods,” Komp. Matematika, No. 3, 80–88 (2013).

  7. A. N. Khimich and V. V. Polyanko, “Optimization of parallel iterative process for the linear systems with sparse matrices,” Teoriya Optym. Rishen’, No. 10, 47–53 (2011).

  8. A. N. Khimich and V. A. Sydoruk, “Hybrid algorithm for linear least squares problem with sparse semidefinite matrix,” Teoriya Optym. Rishen’, 106–113 (2014).

  9. A. N. Khimich and M. F. Yakovlev, “The total error in calculating linear mathematical models by iterative methods,” Cybern. Syst. Analysis. Vol. 38, No. 5, 749–758 (2002). https://doi.org/10.1023/A:1021895010938.

    Article  MATH  Google Scholar 

  10. A. N. Khimich, “Estimates of the total error of in solving systems of linear algebraic equations for matrices of arbitrary ranks,” Komp. Matematika, No. 2, 41–49 (2002).

  11. I. V. Sergienko, A. N. Khimich, and M. F. Yakovlev, “Methods for obtaining reliable solutions to systems of linear algebraic equations,” Cybern. Syst. Analysis,. Vol. 47, No. 1, 62–73 (2011). https://doi.org/10.1007/s10559-011-9290-x.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. N. Khimich and E. A. Nikolaevskaya, “Reliability analysis of computer solutions of systems of linear algebraic equations with approximate initial data,” Cybern. Syst. Analysis, Vol. 44, No. 6, 863–874 (2008). https://doi.org/10.1007/s10559-008-9062-4.

    Article  MATH  Google Scholar 

  13. E. Nikolaevskaya, A. Khimich, and T. Chistyakova, Programming with Multiple Precision; Ser. Studies in Computational Intelligence, Vol. 397, Springer, Berlin–Heidelberg (2012).

  14. O. M. Khimich and T. V. Chistyakova, “Automatic research and solving of linear systems using increased accuracy,” in: Informatics and Systems Sciences (ISS 2016): Proc. of the All-Ukrainian Scientific-Practical Conf. with International Participation (Poltava, Ukraine, 19–21 March, 2015), PUET, Poltava (2015), pp. 365–367.

  15. A. Buttari, J. Langou, J. Kurzak, and J. Dongarra, “A class of parallel tiled linear algebra algorithms for multicore architectures,” Parallel Computing, Vol. 35, Iss. 1, 38–53 (2009). https://doi.org/10.1016/j.parco.2008.10.002.

  16. O. M. Khimich and V. A. Sydoruk, “Using mixed precision in mathematical modeling,” Matem. ta Komp. Modelyuvannya, Ser. Fiz.-Mat. Nauky, Issue 19, 180–187 (2019). https://doi.org/10.32626/2308-5878.2019-19.180-187.

  17. A. Khimich, V. Sydoruk, and P. Yershov, “Intellectualization of computation based on neural networks for mathematical modeling,” in: 2019 IEEE Intern. Conf. on Advanced Trends in Inform. Theory (ATIT), IEEE (2019), pp. 445–448. https://doi.org/10.1109/ATIT49449.2019.9030444.

  18. SCIT Supercomputer of V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine. URL: http://icybcluster.org.ua.

  19. A. N. Khimich, V. V. Polyanko, A. V. Popov, and O. V. Rudich, “The solving of problems of structural analysis on MIMD-computer,” Artificial Intelligence, No. 3, 750–760 (2008).

    Google Scholar 

  20. A. N. Khimich, I. N. Molchanov, V. I. Mova, O. L. Perevozchikova, V. A. Stryuchenko, A. V. Popov, T. V. Chistyakova, M. F. Yakovlev, T. A. Gerasimova, V. S. Zubatenko, A. V. Gromovsky, A. N. Nesterenko, V. V. Polyanko, O. V. Rudich, R. A. Yushchenko, A. A. Nikolaychuk, A. S. Gorodetsky, Ya. E. Slobodyan, and Yu. D. Geraymovich, Numerical Software of the Intelligent MIMD Computer “Inparkom” [in Russian], Naukova Dumka, Kyiv (2007).

    Google Scholar 

  21. V. I. Makhnenko, A. V. Popov, A. P. Semenov, A. N. Khimich, and and M. F. Yakovlev, “Mathematical modeling of physical processes in welding on MIMD computers,” USiM, No. 6, 80–87 (2007).

    Google Scholar 

  22. E. A. Velikoivanenko, A. S. Milenin, A. V. Popov, V. A. Sidoruk, and A. N. Khimich, “Methods of numerical forecasting of serviceability of welded structures on computers of hybrid architecture,” Cybern. Syst. Analysis, Vol. 55, No. 1, 117–127 (2019). https://doi.org/10.1007/s10559-019-00117-8.

    Article  Google Scholar 

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    O. M. Khimich, T. V. Chistyakova, V. A. Sidoruk & P. S. Yershov

Authors
  1. O. M. Khimich
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  2. T. V. Chistyakova
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  3. V. A. Sidoruk
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  4. P. S. Yershov
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Corresponding author

Correspondence to O. M. Khimich.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2021, pp. 162–171.

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Khimich, O.M., Chistyakova, T.V., Sidoruk, V.A. et al. Adaptive Computer Technologies for Solving Problems of Computational and Applied Mathematics. Cybern Syst Anal 57, 990–997 (2021). https://doi.org/10.1007/s10559-021-00424-z

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  • DOI: https://doi.org/10.1007/s10559-021-00424-z

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