Skip to main content
SpringerLink
Log in

Construction of Sequences of Embedded Cubature Formulae for Circular Symmetric Planar Regions

  • Chapter
Numerical Integration

Part of the book series: NATO ASI Series ((ASIC,volume 203))

Abstract

The construction of a cubature formula requires the solution of a large system of nonlinear equations for determining the knots and weights. The number of equations and unknowns can be reduced by imposing some structure on the formula. We construct cubature formulae for circular symmetric regions, with knots on regular polygons. Due to our special structure, we obtain a reduction of the number of equations and unknowns and the systems of nonlinear equations can be solved automatically and quickly. In this paper an algorithm is described and used to construct cubature formulae and sequences of embedded cubature formulae.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Cools and A. Haegemans, ‘Optimal Addition of Knots to Cubature Formulae for Planar Regions’, Numer. Math. 49, pp 269–274 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Cools and A. Haegemans, ‘Automatic computation of knots and weights of cubature formulae for circular symmetric planar regions’, Report TW 77 (K. U. Leuven, 1986).

    Google Scholar 

  3. R. Cools and A. Haegemans, Tables of sequences of cubature formulae for circular symmetric planar regions’, Report TW 83 (K. U. Leuven, 1986).

    Google Scholar 

  4. L. Flatto, ‘Invariants of finite reflection groups’, L’enseignement Math. 24 (1978) pp 237–292.

    MathSciNet  MATH  Google Scholar 

  5. G. Monegato, ‘An overview of results and questions related to Kronrod schemes’, Numerische Integration, ed G. Hammerlin, (Basel,1979) pp 231–240.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Leuven, Celestijnenlaan 200A, B3030, Heverlee, Belgium

    Ronald Cools & Ann Haegemans

Authors
  1. Ronald Cools
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ann Haegemans
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada

    Patrick Keast

  2. Departments of Mathematics and Engineering Mechanics, University of Kentucky, Lexington, Kentucky, USA

    Graeme Fairweather

Rights and permissions

Reprints and permissions

Copyright information

© 1987 D. Reidel Publishing Company

About this chapter

Cite this chapter

Cools, R., Haegemans, A. (1987). Construction of Sequences of Embedded Cubature Formulae for Circular Symmetric Planar Regions. In: Keast, P., Fairweather, G. (eds) Numerical Integration. NATO ASI Series, vol 203. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3889-2_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3889-2_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8227-3

  • Online ISBN: 978-94-009-3889-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation