How to increase convergence order of Newton's method to $2\times m$?

Details How to increase convergence order of Newton's method to $2\times m$? How to increase convergence order of Newton's method to $2\times m$?

2009-12-21

arxiv.org/abs/0912.4140v1

Mathematics

Numerical Analysis

10 pages, 0 figures

Scientific paper

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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