Choosing weight functions in iterative methods for simple roots
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Weight functions with a parameter are introduced into an iteration process to increase the order of the convergence and enhance the behavior of the iteration process. The parameter can be chosen to restrict extraneous fixed points to the imaginary axis and provide the best basin of attraction. The process is demonstrated on several examples.
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2013.11.084
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