Advertisement

Numerische Mathematik

, Volume 62, Issue 1, pp 305–319 | Cite as

Convergence of sequential and asynchronous nonlinear paracontractions

  • L. Elsner
  • I. Koltracht
  • M. Neumann
Article

Summary

We establish the convergence of sequential and asynchronous iteration schemes for nonlinear paracontracting operators acting in finite dimensional spaces. Applications to the solution of linear systems of equations with convex constraints are outlined. A first generalization of one of our convergence results to an infinite pool of asymptotically paracontracting operators is also presented.

Mathematics Subject Classifications (1991)

MSC 1991 65F10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bru, R., Elsner, L., Neumann, M. (1988): Models of parallel chaotic iteration methods. Linear Algebra Appl.102, 175–192Google Scholar
  2. 2.
    De Pierro, A., Iusem, A. (1990): On the asymptotic behavior of some alternate smoothing series expansion iterative methods. Linear Algebra Appl.130, 3–24Google Scholar
  3. 3.
    Elsner, L., Koltracht, I., Neumann, M. (1990): On the convergence of asynchronous paracontractions with applications to tomographic reconstruction from incomplete data. Linear Algebra Appl.130, 65–82Google Scholar
  4. 4.
    Koltracht, I., Lancaster, P. (1990): Constraining Strategies for linear iterative processes. IMA J. Numer. Anal.10, 555–567Google Scholar
  5. 5.
    Nelson, S., Neumann, M. (1987): Generalization of the projection method with applications to SOR method for Hermitian positive semidefinite linear systems. Numer. Math.51, 123–141Google Scholar
  6. 6.
    Ortega, J.M., Rheinboldt, W.C. (1970): Iterative solution of nonlinear equations in several variables. Academic Press, New YorkGoogle Scholar
  7. 7.
    Youla, D.C. (1990): On deterministic convergence of iterations of relaxed projection operators. J. Visual Comm. Image Rep.1,1, 12–20Google Scholar
  8. 8.
    Youla, D.C., Velasco, V. (1986): Extensions of a result on the synthesis of signals in the presence of inconsistent constraints. IEEE Trans. Circuits Syst. CAS-33, 455–468Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • L. Elsner
    • 1
  • I. Koltracht
    • 2
  • M. Neumann
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeld 1Germany
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA

Personalised recommendations