Skip to main content
SpringerLink
Log in
Book cover

Great Lakes CS Conference on New Research Results in Computer Science

Great Lakes CS 1989: Computing in the 90's pp 293–299Cite as

Approximate integration using iterated Levin transformations

  • Track 8: Numerical Analysis
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 507))

Abstract

The efficiency of a quadrature scheme based on iterated Levin U transformations and composite rule approximations for a harmonic sequence of mesh ratios is demonstrated for typical problem classes. Numerical results indicate a favourable comparison with the well known nonlinear extrapolation procedures applied to a sequence of composite quadrature rule sums for a geometric progression of the mesh ratios.

On leave at: California Institute of Technology, Caltech Concurrent Supercomp. Fac., Mail stop 158–79, Pasadena CA 91125; dedonker@wega.caltech.edu

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.L. Cariño, I. Robinson, and E. de Doncker (1989), Approximate integration by the Levin transformation, In preparation.

    Google Scholar 

  2. J.S.R. Chisholm, A. Genz and G.E. Rowlands (1973), Accelerated convergence of quadrature approximations, J. Comp. Phys., v. 10, pp. 284–307.

    Article  MathSciNet  Google Scholar 

  3. E. de Doncker (1978), An adaptive extrapolation algorithm for automatic integration, SIGNUM Newsl., v.13, pp. 12–18.

    Google Scholar 

  4. L. Fox (1967), Romberg integration for a class of singular integrands, Comput. J., v. 10, pp. 87–93.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Fox and L. Hayes (1970), On the definite integration of singular integrals, SIAM Review, v. 12, pp. 449–457.

    Article  MATH  MathSciNet  Google Scholar 

  6. D. Kahaner (1972), Numerical quadrature by the ε algorithm, Math. Comp., v. 26, pp. 689–693.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Levin (1973), Development of non-linear transformations for improving convergence of sequences, Intern. J. Computer Math., v. B3, pp. 371–388.

    Google Scholar 

  8. A. Sidi (1979), Convergence properties of some nonlinear sequence transformations, Math. Comp., v. 33, pp. 315–326.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Wynn (1956), On a device for computing the e m(S n) transformation, Math. Comp., v. 10, pp. 91–96.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. La Trobe University, 3083, Bundoora, VIC, Australia

    Ricolindo Cariño & Ian Robinson

  2. Dept. of Comp. Science, Western Mich. Univ., 49008, Kalamazoo, MI

    Elise de Doncker

Authors
  1. Ricolindo Cariño
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elise de Doncker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ian Robinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Naveed A. Sherwani Elise de Doncker John A. Kapenga

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cariño, R., de Doncker, E., Robinson, I. (1991). Approximate integration using iterated Levin transformations. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038506

Download citation

  • DOI: https://doi.org/10.1007/BFb0038506

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97628-0

  • Online ISBN: 978-0-387-34815-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation