Skip to main content
SpringerLink
Log in

Kronrod and other quadratures

  • Chapter
  • First Online:
Walter Gautschi, Volume 2

Part of the book series: Contemporary Mathematicians ((CM))

  • 1210 Accesses

Abstract

This section is devoted to Gautschi’s work on Kronrod quadratures and other special quadrature rules. For Gauss-type quadrature rules, see Section 15.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Pierre Barrucand. Intégration numérique, abscisse de Kronrod–Patterson et polynômes de Szegő. C. R. Acad. Sci. Paris Sér. A–B, 270:A336–A338, 1970.

    Google Scholar 

  2. Terje O. Espelid. Algorithm 868: globally doubly adaptive quadrature — reliable Matlab codes. ACM Trans. Math. Software, 33(3)21.1–21.21, 2007.

    Google Scholar 

  3. Pedro Gonnet. Increasing the reliability of adaptive quadrature using explicit interpolants. ACM Trans. Math. Software, 37(3):26.1–26.32, 2010.

    Google Scholar 

  4. D. K. Kahaner and G. Monegato. Nonexistence of extended Gauss–Laguerre and Gauss–Hermite quadrature rules with positive weights. Z. Angew. Math. Phys., 29(6):983–986, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  5. Aleksandr Semenovich Kronrod. Nodes and weights of quadrature formulas. Sixteen-place tables, “Nauka”, Moscow, 1964 (Russian). English translation, Consultants Bureau, New York, 1965.

    Google Scholar 

  6. Ravindra Kumar and M. K. Jain. Quadrature formulas for semi-infinite integrals. Math. Comp., 28(126):499–503, 1974. [Table errata: ibid. 56(193):407, 1991].

    Google Scholar 

  7. Giovanni Monegato. A note on extended Gaussian quadrature rules. Math. Comp., 30(136):812–817, 1976.

    Google Scholar 

  8. Giovanni Monegato. Positivity of the weights of extended Gauss–Legendre quadrature rules. Math. Comp., 32(141):243–245, 1978.

    Google Scholar 

  9. Giovanni Monegato. Stieltjes polynomials and related quadrature rules. SIAM Rev., 24(2):137–158, 1982.

    Google Scholar 

  10. G. Monegato and L. Scuderi. Quadrature rules for unbounded intervals and their application to integral equations. In Approximation and Computation 185–208, Springer Optim. Appl., 42, Springer, New York, 2011.

    Google Scholar 

  11. I. P. Mysovskih. A special case of quadrature formulae containing preassigned nodes (Russian). Vesci Akad. Navuk BSSR Ser. Fiz.-Tehn. Navuk, 4:125–127, 1964.

    MathSciNet  Google Scholar 

  12. Sotirios E. Notaris. Gauss–Kronrod quadrature formulae for weight functions of Berstein–Szegő type. II. J. Comput. Appl. Math., 29(2):161–169, 1990.

    Google Scholar 

  13. Franz Peherstorfer. Weight functions admitting repeated positive Kronrod quadrature. BIT 30(1):145–151, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  14. Franz Peherstorfer. On Stieltjes polynomials and Gauss–Kronrod quadrature. Math. Comp., 55(192):649–664, 1990.

    Google Scholar 

  15. Franz Peherstorfer and Knut Petras. Ultraspherical Gauss–Kronrod quadrature is not possible for λ > 3. SIAM J. Numer. Anal., 37(3):927–948, 2000.

    Google Scholar 

  16. B. de la Calle Ysern and F. Peherstorfer. Ultraspherical Stieltjes polynomials and Gauss–Kronrod quadrature behave nicely for λ < 0. SIAM J. Numer. Anal., 45(2):770–786, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ju. S. Ramskiǐ. The improvement of a certain quadrature formula of Gauss type (Russian). Vyčisl. Prikl. Mat. (Kiev), 22:143–146, 1974.

    Google Scholar 

  18. L.F. Shampine. Vectorized adaptive quadrature in Matlab. J. Comput. Appl. Math., 211(2):131–140, 2008.

    Google Scholar 

  19. T. J. Stieltjes. Correspondance d’Hermite et de Stieltjes. II, 439–441. Gauthier-Villars, Paris, 1905.

    Google Scholar 

  20. G. Szegő. Über gewisse orthogonale Polynome, die zu einer oszillierenden Belegungsfunktion gehören. Math. Ann., 110:501–513, 1935.

    Article  MathSciNet  Google Scholar 

  21. Walter Van Assche and Ingrid Vanherwegen. Quadrature formulas based on rational interpolation. Math. Comp., 61(204):765-783, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Torino, Torino, Italy

    Giovanni Monegato

Authors
  1. Giovanni Monegato
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Villeneuve d’Ascq, France

    Claude Brezinski

  2. Department of Computer Science, Purdue University, West Lafayette, Indiana, USA

    Ahmed Sameh

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Monegato, G. (2014). Kronrod and other quadratures. In: Brezinski, C., Sameh, A. (eds) Walter Gautschi, Volume 2. Contemporary Mathematicians. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7049-6_4

Download citation

Publish with us

Policies and ethics

Search

Navigation