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

Abstract

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.