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Numerische Mathematik

, Volume 44, Issue 2, pp 309–315 | Cite as

Nonlinear successive over-relaxation

  • M. E. Brewster
  • R. Kannan
Article

Summary

We study the convergence of Gauss-Seidel and nonlinear successive overrelaxation methods for finding the minimum of a strictly convex functional defined onR n .

Subject Classifications

AMS(MOS): 65H10 CR: 5.15 

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References

  1. 1.
    Concus, P.: Numerical solution of the minimal surface equation. Math. Comput.21, 340–350 (1967)Google Scholar
  2. 2.
    Concus, P., Golub, G.H., O'Leary, D.P.: Numerical solution of nonlinear elliptic partial differential equations. Computing19, 321–329 (1978)Google Scholar
  3. 3.
    Decker, D.W., Kelley, C.T.: Newton's method at singular points. SIAM J. Numer. Anal.17, 66–70 (1980)Google Scholar
  4. 4.
    Greenspan, D.: On approximating extremals of functionals. ICC Bulletin4, 99–120 (1965)Google Scholar
  5. 5.
    Keller, H.B.: Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Application of Bifurcation Theory. Rabinowitz, P. H. (ed.) New York, Academic Press 1977Google Scholar
  6. 6.
    Lieberstein, H.M.: Overrelaxation for nonlinear elliptic partial differential equations. MRC Tech. Report #80 (1959)Google Scholar
  7. 7.
    Rall, L.B.: Convergence of the Newton process to multiple solutions. Numer. Math.9, 23–37 (1966)Google Scholar
  8. 8.
    Reddien, G.W.: On Newton's method for singular problems. SIAM J. Numer. Anal.15, 993–996 (1978)Google Scholar
  9. 9.
    Schechter, S.: Iteration methods for nonlinear problems. Trans. Amer. Math. Soc.104, 179–189 (1962)Google Scholar
  10. 10.
    Schechter, S.: Relaxation methods for convex problems. SIAM J. Numer. Anal.5, 601–612 (1968)Google Scholar
  11. 11.
    Warga, J.: Minimizing certain convex functions. J. Soc. Indus. Appl. Math.11, 588–593 (1963)Google Scholar
  12. 12.
    Young, D.M.: Iterative solutions of large linear systems. New York, Academic Press 1971Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • M. E. Brewster
    • 1
  • R. Kannan
    • 1
  1. 1.Department of MathematicsThe University of Texas at ArlingtonArlingtonUSA

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