Skip to main content
SpringerLink
Log in

The Monte-Carlo algorithm for the solving of systems of linear algebraic equations by the Seidel method

  • Mathematics
  • Published:
Vestnik St. Petersburg University: Mathematics Aims and scope Submit manuscript

Abstract

The iteration algorithm is used to solve systems of linear algebraic equations by the Monte-Carlo method. Each next iteration is simulated as a random vector such that its expectation coincides with the Seidel approximation of the iteration process. We deduce a system of linear equations such that mutual correlations of components of the limit vector and correlations of two iterations satisfy them. We prove that limit dispersions of the random vector of solutions of the system exist and are finite.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. M. Ermakov, The Monte Carlo Method and Related Questions (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  2. G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Modeling. Monte Carlo Methods (Akademiya, Moscow, 2006) [in Russian].

    Google Scholar 

  3. T. M. Tovstik, “On solving systems of linear algebraic equations by Gibbs’s method,” Vestn. St. Petersburg Univ.: Math. 44, 317–323 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. A. Belyaeva and S. M. Ermakov, “On the Monte Carlo method with remembering of intermediate results,” Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron., No. 3, 8–11 (1996) [in Russian].

    MATH  Google Scholar 

  5. A. V. Dmitriev and S. M. Ermakov, “Monte Carlo method and asynchronous iterations,” Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron. 59 (4), 517–528 (2014).

    Google Scholar 

  6. B. P. Demidovich and I. A. Maron, Computational mathematics (Nauka, Moscow, 1970; Mir, Moscow, 1981).

    MATH  Google Scholar 

  7. T. M. Tovstik and K. S. Volosenko, “Monte Carlo algorithm for solving systems of algebraic equations by the Seidel’s method,” in Proc. Int. Conf. Advanced Mathematics, Computations and Applications 2015, Novosibirsk, Oct. 19–23, 2015 (Abvei, Novosibirsk, 2015), pp. 771–776 [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russia

    T. M. Tovstik & K. S. Volosenko

Authors
  1. T. M. Tovstik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. S. Volosenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. M. Tovstik.

Additional information

Original Russian Text © T.M. Tovstik, K.S. Volosenko, 2016, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2016, No. 3, pp. 441–449.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tovstik, T.M., Volosenko, K.S. The Monte-Carlo algorithm for the solving of systems of linear algebraic equations by the Seidel method. Vestnik St.Petersb. Univ.Math. 49, 269–276 (2016). https://doi.org/10.3103/S1063454116030122

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1063454116030122

Keywords

Search

Navigation