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On global convergence of iterative methods

Multigrid Methods For Nonlinear Problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 953)

Abstract

We review and extend results on the local convergence of the classical Newton-Kantorovich method. Then we discuss globally convergent damped and inexact Newton methods and point out advantages of using a minimal error conjugate gradient method for the linear systems arising at each Newton step.

Finally application on a nonlinear elliptic problem is considered. A combination of nested iterations, damped inexact Newton method and two-level grid finite element methods for the solution of the linear boundary value problems encountered at each step are discussed.

Keywords

  • Global Convergence
  • Multigrid Method
  • Local Convergence
  • Nest Iteration
  • Newton Step

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.

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References

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© 1982 Springer-Verlag

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Axelsson, O. (1982). On global convergence of iterative methods. In: Ansorge, R., Meis, T., Törnig, W. (eds) Iterative Solution of Nonlinear Systems of Equations. Lecture Notes in Mathematics, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069371

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  • DOI: https://doi.org/10.1007/BFb0069371

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11602-8

  • Online ISBN: 978-3-540-39379-5

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