Skip to main content
SpringerLink
Log in

Decomposition Implementation of Horner’s Scheme for Calculating the Values of Multidimentional Polynomials

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The paper presents a decomposition implementation of Horner’s scheme for calculating the values of multidimensional polynomials, which reduces the problem to calculating a sequence of values of one-dimensional polynomials according to Horner’s scheme. The possibility of using this scheme in a distributed computer environment is studied. The operation of the scheme is exemplified by the problem of constructing approximate analytical solutions of differential equations with a polynomial right-hand side.

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

Fig. 1.

Similar content being viewed by others

REFERENCES

  1. A. P. Afanas’ev, “Continuation of trajectories in optimal control,” Proceedings of the Institute of System Analysis of the Russian Academy of Sciences (KomKniga, Moscow, 2006) [in Russian].

  2. A. P. Afanas’ev and A. S. Tarasov, “Quasi-analytic solution of systems of differential equations with polynomial right-hand sides,” in Proceedings of the Institute of System Analysis of the Russian Academy of Sciences: Problems in Distributed Computing: Distributed Applications, Communications Systems, Mathematical Models, and Optimization (KomKniga, Moscow, 2006), Vol. 25, pp. 165–183 [in Russian].

  3. A. P. Afanas’ev and S. M. Dzyuba, “Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side,” Comput. Math. Math. Phys. 55 (10), 1665–1673 (2015).

    Article  MathSciNet  Google Scholar 

  4. A. P. Afanas’ev and S. M. Dzyuba, “Construction of the minimal sets of differential equations with polynomial right-hand side,” Differ. Equations 51 (11), 1403–1412 (2015).

    Article  MathSciNet  Google Scholar 

  5. D. D. McCracken and W. S. Dorn, Numerical Methods and FORTRAN Programming (Wiley, New York, 1968).

    MATH  Google Scholar 

  6. A. V. Levitin, “Horner scheme and raising to power,” Algorithms: Introduction to Design and Analysis (Williams, Moscow, 2006), pp. 284–291 [in Russian].

    Google Scholar 

  7. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT and McGraw-Hill, New York, 2009).

    MATH  Google Scholar 

  8. T. V. Dikanev, “Calculation of polynomials in several variables.” http://www.tvd-home.ru/numerical/polynom.

  9. M. L. Dowling, “A fast parallel Horner algorithm,” SIAM J. Comput. 19 (1), 133–142 (1990).

    Article  MathSciNet  Google Scholar 

  10. J. M. Peña and T. Sauer, “On the multivariate Horner scheme,” SIAM J. Numer Anal. 37 (4), 1186–1197 (2000).

    Article  MathSciNet  Google Scholar 

  11. J. M. Peña and T. Sauer, “On the multivariate Horner scheme II: Running error analysis,” Computing (Vienna/New York) 65, 313–322 (2000).

    MathSciNet  MATH  Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation (project no. 16-11-10352) and by the Ministry of Education and Science of the Russian Federation (project no. 2.1777.2017/4.6).

Author information

Authors and Affiliations

  1. Institute for Information Transmission Problems, Russian Academy of Sciences, 127994, Moscow, Russia

    A. P. Afanas’ev

  2. Tver State Technical University, 170026, Tver, Russia

    S. M. Dzyuba

Authors
  1. A. P. Afanas’ev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. M. Dzyuba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. P. Afanas’ev or S. M. Dzyuba.

Additional information

Translated by E. Chernokozhin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Afanas’ev, A.P., Dzyuba, S.M. Decomposition Implementation of Horner’s Scheme for Calculating the Values of Multidimentional Polynomials. Comput. Math. and Math. Phys. 60, 179–183 (2020). https://doi.org/10.1134/S0965542520020025

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542520020025

Keywords:

Search

Navigation