How to increase convergence order of Newton's method to $2 imes m$?. (arXiv:0912.4140v1 [math.NA])

We present a simple yet powerful technique for forming iterative methods of
various convergence orders. Methods of various convergence orders (four, six,
eight and ten) are formed through a modest modification of the classical Newton
method. The technique can be easily implemented in existing software packages
as suggested by the presented C$^{++}$ algorithm. Finally some problems are
solved through the proposed algorithm.

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Original source : http://arxiv.org/abs/0912.4140...