Construction of optimal order nonlinear solvers using inverse interpolation
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There is a vast literature on finding simple roots of nonlinear equations by iterative meth- ods. These methods can be classified by order, by the information used or by efficiency. There are very few optimal methods, that is methods of order 2m requiring m + 1 function evaluations per iteration. Here we give a general way to construct such methods by using inverse interpolation and any optimal two-point method. The presented optimal multi- point methods are tested on numerical examples and compared to existing methods of the same order of convergence.
Applied Mathematics and Computation, 217, (2010), 2448-2455.The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2010.07.045
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