New iterative schemes for nonlinear fixed point problems, with applications to problems with bifurcations and incomplete-data problems

Ch Roland, R. Varadhan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we propose a new method which could be considered as a modification of the Δk-method introduced for solving nonlinear fixed point problems. At each iteration of the new scheme, we evaluate the Δk steplength once and we use it twice. Various numerical results illustrate the efficiency of the new scheme. They concern the solution of a reaction-diffusion problem which exhibits a bifurcation. An additional example, involving a mixture of Poisson distributions, will be given and suggest that the new scheme could be adapted with success for an important statistical problem called the expectation-maximization problem.

Original languageEnglish (US)
Pages (from-to)215-226
Number of pages12
JournalApplied Numerical Mathematics
Volume55
Issue number2
DOIs
StatePublished - Oct 1 2005

Keywords

  • Fixed point methods
  • Nonlinear systems
  • Propagation of the error

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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