Skip to main content
Springer Nature Link
Log in

Parallel algorithms and interval selection strategies for globally adaptive quadrature

  • Conference paper
  • First Online:
PARLE'94 Parallel Architectures and Languages Europe (PARLE 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 817))

Abstract

A globally adaptive algorithm for approximating one-dimensional definite integrals on parallel computers is described. The algorithm is implemented on a Kendall Square Research KSR-1 parallel computer and numerical results are presented. The algorithm gives significant speedups on a range of hard problems, including ones with singular integrands. A number of alternatives for the interval selection strategy that is at the core of this algorithm are evaluated.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. J. Bernsten and T. O. Espelid (1988) A Parallel Global Adaptive Quadrature Algorithm for Hypercubes, Parallel Computing, 8 313–323.

    Article  Google Scholar 

  2. J. M. Bull and T. L. Freeman (1993) Parallel Globally Adaptive Quadrature on the KSR-1, N. A. Report No. 228, Department of Mathematics, University of Manchester, to appear in Advances in Computational Mathematics.

    Google Scholar 

  3. J. M. Bull and T. L. Freeman (1994) Parallel Algorithms for Numerical Integration in One and Several Dimensions, to appear in CWI Tracts.

    Google Scholar 

  4. K. Burrage (1990) An Adaptive Numerical Integration Code for a Chain of Transputers, Parallel Computing, 16 305–312.

    Article  Google Scholar 

  5. M. Derakhshan (1993) Private Communication.

    Google Scholar 

  6. G. Fairweather and P. M. Keast (eds.) (1987) Numerical Integration. Recent Developments, Software and Applications, NATO ASI Series C203, D. Reidel, Dordrecht.

    Google Scholar 

  7. A. Genz (1987) The Numerical Evaluation of Multiple Integrals on Parallel Computers, 219–229 of [6].

    Google Scholar 

  8. I. Gladwell, (1987) Vectorisation of One Dimensional Quadrature Codes, 230–238 of [6].

    Google Scholar 

  9. A. S. Kronrod (1965) Nodes and Weights of Quadrature Formulas, Consultants Bureau, New York.

    Google Scholar 

  10. M. A. Malcolm and R. B. Simpson (1975) Local Versus Global Strategies for Adaptive Quadrature, ACM Transactions on Mathematical Software, 1 129–146.

    Article  Google Scholar 

  11. W. M. McKeeman (1962) Adaptive Numerical Integration by Simpson's Rule, Algorithm 145, Communications ACM, 5 604.

    Article  Google Scholar 

  12. N.A.G. (1991) N.A.G. Fortran Library Manual, Mark 15, N.A.G. Ltd., Oxford.

    Google Scholar 

  13. R. Piessens, E. de Doncker, C. überhuber and D. Kahaner (1983) QUADPACK, A Subroutine Package for Automatic Integration, Springer-Verlag.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Novel Computing & Department of Mathematics, University of Manchester, M13 9PL, Manchester, UK

    J. M. Bull & T. L. Freeman

Authors
  1. J. M. Bull
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. L. Freeman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Costas Halatsis Dimitrios Maritsas George Philokyprou Sergios Theodoridis

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bull, J.M., Freeman, T.L. (1994). Parallel algorithms and interval selection strategies for globally adaptive quadrature. In: Halatsis, C., Maritsas, D., Philokyprou, G., Theodoridis, S. (eds) PARLE'94 Parallel Architectures and Languages Europe. PARLE 1994. Lecture Notes in Computer Science, vol 817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58184-7_125

Download citation

  • DOI: https://doi.org/10.1007/3-540-58184-7_125

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58184-0

  • Online ISBN: 978-3-540-48477-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics