Skip to main content
SpringerLink
Log in

On some weight functions admitting (0, 2) quadrature formulae with a high algebraic degree of precision

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

The purpose of this paper is to find a class of weight functions μ for which there exist quadrature formulae of the form

$$\int_{ - 1}^1 {\mu (x) f(x) dx \approx \sum\limits_{k = 1}^n {(a_k f(x_k ) + b_k f''(x_k ))} }$$
((1))

, which are precise for every polynomial of degree 2n.

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. D. K. Dimitrov,On a problem of Turán: (0,2) quadrature formula with a high algebraic degree of precision, Aequationes Math.,41 (1991), 168–171.

    Article  MathSciNet  Google Scholar 

  2. G. G. Lorentz, K. Jetter and S. R. Riemenschneider,Birkhoff interpolation, Encyclopedia of Mathematics and its Applications, vol. 19, Addison-Wesley, 1983.

  3. S. J. Maskell and R. A. Sack,Generalized Lobatto quadrature formulas for contour integrals, Studies in Numerical Analysis (B. K. Scaife ed.), Academic Press, London-New York, 1974, pp. 295–310.

    Google Scholar 

  4. P. Nevai and A. K. Varma,A new quadrature formula associated with the ultraspherical polynomials, J. Approx. Theory,50 (1987), 133–140.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Surányi and P. Turán,Notes on interpolation I, Acta Math. Acad. Sci. Hungar.6 (1955), 67–80.

    Article  MATH  MathSciNet  Google Scholar 

  6. G. Szegö,Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, 4th ed., Amer. Math. Soc., Providence, R.I., 1975.

    MATH  Google Scholar 

  7. P. Turán,On some open problems of Approximation Theory, J. Approx. Theory,29 (1980), 23–85.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Bulgarian Academy of Science, 1113, Sofia, Bulgaria

    Dimitar K. Dimitrov

Authors
  1. Dimitar K. Dimitrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper is supported by The Royal Society Postdoctoral Fellowship Programme and The Bulgarian Ministry of Science under Grant MM-15.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dimitrov, D.K. On some weight functions admitting (0, 2) quadrature formulae with a high algebraic degree of precision. Calcolo 30, 159–170 (1993). https://doi.org/10.1007/BF02576179

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02576179

Keywords

Search

Navigation