New iterative schemes for nonlinear fixed point problems, with applications to problems with bifurcations and incomplete-data problems
New iterative schemes for nonlinear fixed point problems, with applications to problems with bifurcations and incomplete-data problems
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DOI：
10.1016/j.apnum.2005.02.006
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发表时间：
2005-10
影响因子：
2.8
通讯作者：
C. Roland;R. Varadhan
中科院分区：
文献类型：
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作者：
C. Roland;R. Varadhan
本文提出了一种新的方法，它可以看作是对求解非线性不动点问题的Δ k-方法的改进.在新方案的每次迭代中，我们计算一次Δ k步长，并使用它两次。各种数值结果说明了新格式的有效性。它们涉及的反应扩散问题的解决方案，其中表现出分歧。一个额外的例子，涉及泊松分布的混合物，将给出并建议，新的计划可以适应成功的一个重要的统计问题，称为期望最大化问题。
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 Δksteplength 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.