Skip to main content
SpringerLink
Log in
Book cover

Conference on the Numerical Solution of Differential Equations pp 113–132Cite as

On the effects of scaling of the peaceman-rachford method

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 109))

This is a preview of subscription content, 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   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Birkhoff and R. S. Varga, "Implicit alternating direction methods," Trans. Math. Soc., v.92, pp. 13–24.

    Google Scholar 

  2. B. L. Buzbee, G. H. Golub and C. W. Nielson, "The method of odd/even reduction and factorization with application to Poisson's equation," Stanford Computer Science Department report, 1969.

    Google Scholar 

  3. R. Courant and D. Hilbert, "Methods of Mathematical Physics," Interscience, 1953.

    Google Scholar 

  4. J. Douglas Jr., "Alternating direction methods for three space variables," Numer. Math., v.4, 1962, pp. 41–63.

    Article  MathSciNet  MATH  Google Scholar 

  5. G. E. Forsythe and E. G. Straus, "On best conditioned matrices," Proc. Amer. Math. Soc., v.6, 1955, pp. 340–345.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. R. Garabedian, "Partial differential equations," Wiley, 1964.

    Google Scholar 

  7. G. H. Golub, "Comparison of the variance of minimum variance and weighted least squares regression coefficients," The Annals of Math. Statistics, v.34, no.3, 1963, pp. 984–991.

    Article  MathSciNet  MATH  Google Scholar 

  8. W. H. Guillinger Jr., "The Peaceman-Rachford method for small mesh increments," J. Math. Anal. Appl., v.11, 1965, pp. 261–277.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. E. Gunn, "On the two-stage iterative method of Douglas for mildly nonlinear elliptic difference equations," Numer. Math., v.6, 1964, pp. 243–249.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. W. Hockney, "A fast direct solution of Poisson's equation using Fourier analysis," J. ACM., v.12, no.1, 1965, pp. 95–113.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Kahan and J. Varah, "Two working algorithms for the eigenvalues of a symmetric tridiagonal matrix," Stanford Computer Science Department report 1966.

    Google Scholar 

  12. D. W. Peaceman and H. H. Rachford Jr., "The numerical solution of parabolic and elliptic differential equations," J. SIAM, v.3, 1955, pp. 28–41.

    MathSciNet  MATH  Google Scholar 

  13. C. Pearcy, "On the convergence of alternating direction procedures," Numer. Math., v.4, 1962, pp. 172–176.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. van der Sluis, "Condition numbers and equilibration of matrices," to appear.

    Google Scholar 

  15. R. S. Varga, "Matrix Iterative Analysis," Prentice-Hall, 1962.

    Google Scholar 

  16. E. L. Wachspress, "Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics," Prentice-Hall, 1966.

    Google Scholar 

  17. E. L. Wachspress and G. J. Habetler, "An alternating-direction-implicit iteration technique," J. SIAM, 8, 1960, pp. 403–424.

    MathSciNet  MATH  Google Scholar 

  18. O. B. Widlund, "On the rate of convergence of an alternating direction implicit method in a noncommutative case," Math. Comp., v.20, 1966, pp. 500–515.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Olaf B. Widlund
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. Li. Morris

Rights and permissions

Reprints and permissions

Copyright information

© 1969 Springer-Verlag

About this paper

Cite this paper

Widlund, O.B. (1969). On the effects of scaling of the peaceman-rachford method. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060018

Download citation

  • DOI: https://doi.org/10.1007/BFb0060018

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04628-8

  • Online ISBN: 978-3-540-36158-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation