Skip to main content
SpringerLink
Log in

Higher-order polynomial approximation

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

A new approach to polynomial higher-order approximation (smoothing) based on the basic elements method (BEM) is proposed. A BEM polynomial of degree n is defined by four basic elements specified on a three-point grid: x 0 + α < x 0 < x 0 + β, αβ <0. Formulas for the calculation of coefficients of the polynomial model of order 12 were derived. These formulas depend on the interval length, continuous parameters α and β, and the values of f (m)(x 0+ν), ν = α, β, 0, m = 0,3. The application of higher-degree BEM polynomials in piecewise-polynomial approximation and smoothing improves the stability and accuracy of calculations when the grid step is increased and reduces the computational complexity of the algorithms.

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. P. L. Chebyshev, Selected Works (Akad. Nauk SSSR, Moscow, 1955) [in Russian].

    Google Scholar 

  2. Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline-Functions (Nauka, Moscow, 1980), p. 267 [in Russian].

    MATH  Google Scholar 

  3. N. D. Dikoussar, “Function parameterization by using 4-point transforms,” Comp. Phys. Commun. 99, 235–254 (1997).

    Article  MATH  Google Scholar 

  4. N. D. Dikusar, “The basic element method,” Math. Models Comput. Simul. 3, 492–507 (2011).

    Article  MathSciNet  Google Scholar 

  5. N. N. Kalitkin and N. M. Shlyakhov, “B-splines of arbitrary degree,” Dokl. Math. 60, 28–31 (1999).

    MathSciNet  MATH  Google Scholar 

  6. C. de Boor, A Practical Guide to Splines (Springer, Berlin, 1978).

    Book  MATH  Google Scholar 

  7. N. D. Dikusar, “Piecewise polynomial approximation of the sixth order with automatic knots detection,” Math. Models Comput. Simul. 6, 509–522 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Franke, “Scattered data interpolation: tests of some methods,” Math. Comput., No. 38, 181–200 (1982).

    MathSciNet  MATH  Google Scholar 

  9. “Review of particle physics,” Eur. Phys. J. C, 235 (2000).

Download references

Author information

Authors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, 141980, Russia

    N. D. Dikusar

Authors
  1. N. D. Dikusar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. D. Dikusar.

Additional information

Original Russian Text © N.D. Dikusar, 2015, published in Matematicheskoe Modelirovanie, 2015, Vol. 27, No. 9, pp. 89–109.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dikusar, N.D. Higher-order polynomial approximation. Math Models Comput Simul 8, 183–200 (2016). https://doi.org/10.1134/S2070048216020058

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048216020058

Keywords

Search

Navigation