Skip to main content
SpringerLink
Log in

Error Estimates and Convergence Acceleration

  • Chapter
Book cover Error Control and Adaptivity in Scientific Computing

Part of the book series: NATO Science Series ((ASIC,volume 536))

  • 250 Accesses

Abstract

When a sequence (S n ) converges too slowly to its limit S, it can transformed into a new sequence (T n ) by a sequence transformation T. Under some assumptions, (T n ) converges to the same limit S and, under some additional assumptions, (T n ) converges faster than (S n ), that is, for a scalar sequence,

$$ \mathop {\lim }\limits_{n \to \infty } (T_n - S)/(S_n - S) = 0. $$

In that case T is said to accelerate the covergence of (S n ).

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. Bellalij, M. (1990) A simultaneous process for convergence acceleration and error control, J. Cornput. Appl. Math. 33, pp. 217–231.

    Article  MathSciNet  MATH  Google Scholar 

  2. Brezinski, C. (1983) Error control in convergence acceleration processes, IMA J. Nurner. Anal. 3, pp. 65–80.

    Article  MathSciNet  MATH  Google Scholar 

  3. Brezinski, C. (1988) A new approach to convergence acceleration methods, in A. Cuyt (ed.), Nonlinear Numerical Methods and Rational Approximation, Reidel, Dordrecht, pp. 373–405.

    Chapter  Google Scholar 

  4. Brezinski, C. and Matos, A.C. (1996) A derivation of extrapolation algorithms based on error estimates, J. Comput. Appl. Math., 66, pp. 5–26.

    Article  MathSciNet  MATH  Google Scholar 

  5. Brezinski, C. and Redivo Zaglia, M. (1991) Extrapolation Methods. Theory and Practice. North-Holland, Amsterdam.

    Google Scholar 

  6. Brezinski, C. and Redivo Zaglia, M. (1991) Construction of extrapolation processes, Appl. Numer. Math., 8, pp. 11–23

    Article  MathSciNet  MATH  Google Scholar 

  7. Matos, A.C. (1989) Acceleration methods for sequences such that, in W.F. Ames and C. Brezinski (eds.), Numerical and Applied Mathematics, vol. 1.2, Baltzer, Basel, pp. 447–451.

    Google Scholar 

  8. Matos, A.C. (1990) A convergence acceleration method based on a good estimation of the absolute error, IMA J. Numer. Anal., 10, pp. 243–251.

    Article  MathSciNet  MATH  Google Scholar 

  9. Matos, A.C. (1990) Extrapolation algorithms based on the asymptotic expansion of the inverse of the error; application to continued fractions, J. Comput. Appl. Math., 32, pp. 179–190.

    Article  MathSciNet  MATH  Google Scholar 

  10. Weniger, E.J. (1989) Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Reports, 10, pp. 189–371.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire d’Analyse Numérique et d’Optimisation, Université des Sciences et Technologies de Lille, 59655-Villeneuve d’Ascq cedex, France

    C. Brezinski

Authors
  1. C. Brezinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Center of Applied Mathematics, Selcuk University, Konya, Turkey

    Haydar Bulgak

  2. Institut für Informatik, Technische Universität München, D-80290, München, Germany

    Christoph Zenger

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Brezinski, C. (1999). Error Estimates and Convergence Acceleration. In: Bulgak, H., Zenger, C. (eds) Error Control and Adaptivity in Scientific Computing. NATO Science Series, vol 536. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4647-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4647-0_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5809-1

  • Online ISBN: 978-94-011-4647-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation