Advertisement

Numerische Mathematik

, Volume 25, Issue 3, pp 231–238 | Cite as

Error analysis for a class of degenerate-kernel methods

  • Ian H. Sloan
Article

Summary

Convergence theorems are proved for a recently proposed class of degenerate-kernel methods for the numerical solution of Fredholm integral equations of the second kind. In particular, it is shown that the simplest of these methods has a faster rate of convergence than the simple method of moments, or Galerkin method, even though its computational requirements are almost identical.

Keywords

Integral Equation Mathematical Method Fast Rate Error Analysis Convergence Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atkinson, K. E.: A survey of numerical methods for the solution of Fredholm integral equations of the second kind. Proceedings of the SIAM symposium “Numerical solution of integral equations with physical applications”, Madison, Wisconsin, 1971: To be publishedGoogle Scholar
  2. 2.
    Kantorovich, L. V., Krylov, V. I.: Approximate methods of higher analysis. Groningen: P. Noordhoff 1958Google Scholar
  3. 3.
    Mikhlin, S. G.: Variational methods in mathematical physics Oxford: Pergamon Press 1964Google Scholar
  4. 4.
    Mikhlin, S. G., Smolitskiy, K. L.: Approximate methods for solution of differential and integral equations. New York: American Elsevier 1967Google Scholar
  5. 5.
    Riesz, F., Sz.-Nagy, B.: Functional analysis. New York: Frederick Ungar 1955Google Scholar
  6. 6.
    Sloan, I. H., Burn, B. J., Datyner, N.: A new approach to the numerical solution of integral equations. J. of Computational Physics18, 92–105 (1975)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Ian H. Sloan
    • 1
  1. 1.Dept. of Applied MathematicsUniv. of New South WalesKensingtonAustralia

Personalised recommendations